SELINA Solutions for Class 10 Maths Chapter 5 - Quadratic Equations

Aim for top marks in the prelim and board exams with the Selina Solutions for ICSE Class 10 Mathematics Chapter 5 Quadratic Equations. Improve your analytical abilities to prove whether the given equation is a quadratic equation or not using our textbook solutions. Also, learn the concept of two equal roots and two distinct real roots through Maths practice.

Revise the quadratic formula and the factorisation method to prove quadratic equations with the support of our ICSE Class 10 Maths textbook solutions. To revisit the problem-solving methods, you can watch our concept videos or go through our well-written revision notes.

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Chapter 5 - Quadratic Equations Exercise Ex. 5(A)

Question 1(iv)

x2 + 5x - 5 = (x - 3)2

Solution 1(iv)

x2 + 5x - 5 = (x - 3)2

x2 + 5x - 5 = x2 - 6x + 9

11x - 14 =0; which is not of the form ax2 + bx + c = 0.

Given equation is not a quadratic equation. 

Question 1(v)

7x3 - 2x2 + 10 = (2x - 5)2

Solution 1(v)

7x3 - 2x2 + 10 = (2x - 5)2

7x3 - 2x2 + 10 = 4x2 - 20x + 25

7x3 - 6x2 + 20x - 15 = 0; which is not of the form ax2 + bx + c = 0.

Given equation is not a quadratic equation.

 

Question 1(vi)

(x - 1)2 + (x + 2)2 + 3(x +1) = 0

Solution 1(vi)

(x - 1)2 + (x + 2)2 + 3(x +1) = 0

x2 - 2x + 1 + x2 + 4x + 4 + 3x + 3 = 0

2x2 + 5x + 8 = 0; which is of the form ax2 + bx + c = 0.

Given equation is a quadratic equation.

 

Question 1(i)

Find which of the following equations are quadratic:

(3x - 1)2 = 5(x + 8)

Solution 1(i)

(3x - 1)2 = 5(x + 8)

(9x2 - 6x + 1) = 5x + 40

9x2 - 11x - 39 =0; which is of the form ax2 + bx + c = 0.

Given equation is a quadratic equation.

Question 1(ii)

5x2 - 8x = -3(7 - 2x)

Solution 1(ii)

5x2 - 8x = -3(7 - 2x)

5x2 - 8x = 6x - 21

5x2 - 14x + 21 =0; which is of the form ax2 + bx + c = 0.

Given equation is a quadratic equation.

 

Question 1(iii)

(x - 4)(3x + 1) = (3x - 1)(x +2)

Solution 1(iii)

(x - 4)(3x + 1) = (3x - 1)(x +2)

3x2 + x - 12x - 4 = 3x2 + 6x - x - 2

16x + 2 =0; which is not of the form ax2 + bx + c = 0.

Given equation is not a quadratic equation. 

Question 2(i)

Is x = 5 a solution of the quadratic equation x2 - 2x - 15 = 0?

Solution 2(i)

x2 - 2x - 15 = 0

For x = 5 to be solution of the given quadratic equation it should satisfy the equation.

So, substituting x = 5 in the given equation, we get

L.H.S = (5)2 - 2(5) - 15

 = 25 - 10 - 15

 = 0

 = R.H.S

Hence, x = 5 is a solution of the quadratic equation x2 - 2x - 15 = 0. 

Question 2(ii)

Is x = -3 a solution of the quadratic equation 2x2 - 7x + 9 = 0?

Solution 2(ii)

2x2 - 7x + 9 = 0

For x = -3 to be solution of the given quadratic equation it should satisfy the equation

So, substituting x = 5 in the given equation, we get

L.H.S=2(-3)2 - 7(-3) + 9

 = 18 + 21 + 9    

 = 48 

  R.H.S

Hence, x = -3 is not a solution of the quadratic equation 2x2 - 7x + 9 = 0. 

Question 3

If Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations is a solution of equation 3x2 + mx + 2 = 0, find the value of m.

Solution 3

For x = Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations to be solution of the given quadratic equation it should satisfy the equation

So, substituting x = Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations in the given equation, we get

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations and 1 are the solutions of equation mx2 + nx + 6 = 0. Find the values of m and n.

Solution 4

For x = Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations and x = 1 to be solutions of the given quadratic equation it should satisfy the equation

So, substituting x = Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations and x = 1 in the given equation, we get

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solving equations (1) and (2) simultaneously,

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

If 3 and -3 are the solutions of equation ax2 + bx - 9 = 0. Find the values of a and b.

Solution 5

For x = 3 and x = -3 to be solutions of the given quadratic equation it should satisfy the equation

So, substituting x = 3 and x = -3 in the given equation, we get

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solving equations (1) and (2) simultaneously,

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 5 - Quadratic Equations Exercise Ex. 5(B)

Question 1

Without solving, comment upon the nature of roots of each of the following equations :

(i)7x2 - 9x +2 =0 (ii)6x2 - 13x +4 =0

 

(iii)25x2 - 10x +1=0 (iv)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 

(v)x2 - ax - b2 =0 (vi)2x2 +8x +9=0

Solution 1

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations


Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations


Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 2(i)

Find the value of p, if the following quadratic equation has equal roots : 4x2 - (p - 2)x + 1 = 0

Solution 2(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 2(ii)

Find the value of 'p', if the following quadratic equations have equal roots :

x2 + (p - 3)x + p = 0

Solution 2(ii)

x2 + (p - 3)x + p = 0

 Here, a = 1, b = (p - 3), c = p

 Since, the roots are equal,

b2- 4ac = 0

(p - 3)2- 4(1)(p) = 0

p2 + 9 - 6p - 4p = 0

p2- 10p + 9 = 0

p2-9p - p + 9 = 0

p(p - 9) - 1(p - 9) = 0

(p -9)(p - 1) = 0

p - 9 = 0 or p - 1 = 0

p = 9 or p = 1 

Question 3

The equation 3x2 - 12x + (n - 5)=0 has equal roots. Find the value of n.

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Find the value of m, if the following equation has equal roots : (m - 2)x2 - (5+m)x +16 =0

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Find the value of k for which the equation 3x2- 6x + k = 0 has distinct and real roots.

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 5 - Quadratic Equations Exercise Ex. 5(C)

Question 1

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

2x2 - 9x + 10 = 0, When

(i) x N

(ii) x Q

Solution 16

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

Find the quadratic equation, whose solution set is :

(i)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations (ii)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 22(i)

 Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 22(ii)

 Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

Find the value of x, if a + 1=0 and x2 + ax - 6 =0.

Solution 23

If a+1=0, then a = -1

Put this value in the given equation x2 + ax - 6 =0

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

Find the value of x, if a + 7=0; b + 10=0 and 12x2 = ax - b.

Solution 24

If a + 7 =0, then a = -7

and b + 10 =0, then b = - 10

 

Put these values of a and b in the given equation

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

Use the substitution y= 2x +3 to solve for x, if 4(2x+3)2 - (2x+3) - 14 =0.

Solution 25

4(2x+3)2 - (2x+3) - 14 =0

Put 2x+3 = y

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 26

Without solving the quadratic equation 6x2 - x - 2=0, find whether Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations is a solution of this equation or not.

Solution 26

Consider the equation, 6x2 - x - 2=0

Put Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations in L.H.S.

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Since L.H.S.= R.H.S., then Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations is a solution of the given equation.

Question 27

Determine whether x = -1 is a root of the equation x2 - 3x +2=0

or not.

Solution 27

x2 - 3x +2=0

Put x = -1 in L.H.S.

L.H.S. = (-1)2 - 3(-1) +2

= 1 +3 +2=6 Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic EquationsR.H.S.

Then x = -1 is not the solution of the given equation.

Question 28

If x =Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations is a solution of the quadratic equation 7x2+mx - 3=0;

Find the value of m.

Solution 28

7x2+mx - 3=0

Given x = Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations is the solution of the given equation.

Put given value of x in the given equation

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 29

If x = -3 and x = Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations are solutions of quadratic equation mx2 + 7x + n = 0, find the values of m and n.

Solution 29

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 30

If quadratic equation x2 - (m + 1) x + 6=0 has one root as x =3;

find the value of m and the root of the equation.

Solution 30

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 31

Given that 2 is a root of the equation 3x2 - p(x + 1) = 0 and that the equation px2 - qx + 9 = 0 has equal roots, find the values of p and q.

Solution 31

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 32

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 32

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations


or x = -(a + b)

Question 33

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 33

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 34

If -1 and 3 are the roots of x2+px+q=0
then find the values of p and q

Solution 34

 Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 5 - Quadratic Equations Exercise Ex. 5(D)

Question 1

Solve each of the following equations using the formula :

 

(i)x2 - 6x =27 (ii)x2 - 10x +21=0

 

(iii)x2 +6x - 10 =0 (iv)x2 +2x - 6=0

 

(v)3x2+ 2x - 1=0 (vi)2x2 + 7x +5 =0

 

(vii)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations (viii) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(ix) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations (x) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(xi) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations (xii) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(xiii)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations (xiv)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Solve each of the following equations for x and give, in each case, your answer correct to one decimal place :

(i)x2 - 8x+5=0

(ii)5x2 +10x - 3 =0

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations


Question 3(iv)

x2 - 5x - 10 = 0

Solution 3(iv)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 3(iii)

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

x2 - 3x - 9 =0

Solution 3(iii)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations



Question 3(ii)

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations



Question 3(i)

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

(i)2x2 - 10x +5=0

Solution 3(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Solve each of the following equations for x and give, in each case, your answer correct to 3 decimal places :

(i)3x2 - 12x - 1 =0

(ii)x2 - 16 x +6= 0

(iii)2x2 + 11x + 4= 0

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Solve:

(i)x4 - 2x2 - 3 =0

(ii)x4 - 10x2 +9 =0

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations


Question 6

Solve :

(i)(x2 - x)2 + 5(x2 - x)+ 4=0

(ii)(x2 - 3x)2 - 16(x2 - 3x) - 36 =0

Solution 6

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations


Question 7

Solve :

(i)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(ii)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(iii)Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 

Question 8

Solve the equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations. Write your answer correct to two decimal places.

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Solve the following equation and give your answer correct to 3 significant figures:

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Consider the given equation:

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 

 

Question 10

Solve for x using the quadratic formula. Write your answer correct to two significant figures.

(x - 1)2 - 3x + 4 = 0

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Solve the quadratic equation x2 - 3(x + 3) = 0; Give your answer correct to two significant figures.

Solution 11

x2 - 3(x + 3) = 0

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations 

Chapter 5 - Quadratic Equations Exercise Ex. 5(E)

Question 1

Solve: 

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Solve: (2x+3)2=81

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

Solve each of the following equations, giving answer upto two decimal places.(i)x2 - 5x -10=0(ii) 3x2 - x - 7 =0

Solution 12

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations


Question 13

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

Solve :

(i)x2 - 11x - 12 =0; when x Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic EquationsN

 

(ii)x2 - 4x - 12 =0; when x Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic EquationsI

 

(iii)2x2 - 9x + 10 =0; when x Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic EquationsQ

Solution 14

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations



Question 15

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 


Question 18

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations



Question 19

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

Consider the given equation:

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 

 

Chapter 5 - Quadratic Equations Exercise Ex. 5(F)

Question 1(i)

Solve : (x+5)(x-5)=24 

Solution 1(i)

Given: (x+5)(x-5)=24

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations 

Question 1(ii)

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations 

Solution 1(ii)

Given: Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations 

Question 1(iii)

Solve : Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations 

Solution 1(iii)

Given: Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations or Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations 

Question 2

One root of the quadratic equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations. Find the value of m. Also, find the other root of the equation. 

Solution 2

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations …. (i)

One of the roots of (i) is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations, so it satisfies (i)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

So, the equation (i) becomes Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Hence, the other root isSelina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations.

Question 3

One root of the quadratic equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations is -3, find its other root. 

Solution 3

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations …. (i)

One of the roots of (i) is -3, so it satisfies (i)

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Hence, the other root is 2a.

Question 4

If Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equationsand Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations;find the values of x. 

Solution 4

Given Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations i.e Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

So, the given quadratic equation becomes

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Hence, the values of x are Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations andSelina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations.

Question 5

Find the solution of the equationSelina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations; if Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equationsand Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations. 

Solution 5

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations….. (i)

Also, given Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equationsand Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations and Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

So, the equation (i) becomes

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Hence, the solution of given quadratic equation are Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations andSelina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations.

Question 6

If m and n are roots of the equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equationswhere x ≠ 0 and x ≠ 2; find m × n. 

Solution 6

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Since, m and n are roots of the equation, we have

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations and Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations.

Question 7

Solve, using formula :

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations 

Solution 7

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Using quadratic formula,

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

x = a + 1 or x = -a - 2 = -(a + 2)

 

Question 8

Solve the quadratic equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(i) When Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations(integers)

(ii) When Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations(rational numbers) 

Solution 8

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(i) When Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equationsthe equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations has no roots

(ii) When Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equationsthe roots of Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations are

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equationsor Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Find the value of m for which the equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations has real and equal roots. 

Solution 9

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

The quadratic equation has real and equal roots if its discriminant is zero.

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations or Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Find the values of m for which equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations has equal roots. Also, find the roots of the given equation. 

Solution 10

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations…. (i)

The quadratic equation has equal roots if its discriminant is zero

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

When Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations, equation (i) becomes

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

When Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations, equation (i) becomes

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

 x = Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Find the value of k for which equation Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations has real roots. 

Solution 11

Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations…. (i)

The quadratic equation has real roots if its discriminant is greater than or equal to zero

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Hence, the given quadratic equation has real roots forSelina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations.

Question 12

Find, using quadratic formula, the roots of the following quadratic equations, if they exist

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations 

Solution 12

(i) Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

D = b2 - 4ac =Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations = 25 - 24 = 1

Since D > 0, the roots of the given quadratic equation are real and distinct.

Using quadratic formula, we have

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations or Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

(ii) Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

D = b2 - 4ac =Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations = 16 - 20 = - 4

Since D < 0, the roots of the given quadratic equation does not exist.

Question 13

Solve :

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations and x > 0.

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations and x < 0. 

Solution 13

(i) Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations or Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

But as x > 0, so x can't be negative.

Hence, x = 6.

(ii) Given quadratic equation is Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations or Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations

But as x < 0, so x can't be positive.

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Quadratic Equations