one root of the quadratic equation x^2-12x+a=0 is thrice the other. find the value of a

Asked by amit.clw4 | 22nd May, 2021, 07:08: PM

Expert Answer:

begin mathsize 16px style straight x squared minus 12 straight x space plus space straight a equals space 0
Let space straight alpha space and space straight beta space be space the space roots space of space the space given space quadratic space equation.
According space to space the space condition space given space in space the space question comma space we space get
straight alpha space equals space 3 straight beta space space.... left parenthesis 1 right parenthesis
We space know space that comma
straight alpha space plus space straight beta space equals space fraction numerator negative coefficient space of space straight x over denominator coefficient space of space straight x squared end fraction equals fraction numerator negative open parentheses negative 12 close parentheses over denominator 1 end fraction equals 12 space
From space left parenthesis 1 right parenthesis comma
straight alpha space plus space straight beta space equals space 12 space rightwards double arrow space 4 straight beta space equals space 12 space space rightwards double arrow straight beta space equals space 3

rightwards double arrow straight alpha space equals space 12 space minus space 3 space equals space 9
αβ space equals space fraction numerator constant space term over denominator coefficient space of space straight x squared end fraction equals straight a over 1 equals straight a
rightwards double arrow 9 cross times 3 space equals space straight a
rightwards double arrow straight a space equals space 27
end style

Answered by Yasmeen Khan | 24th May, 2021, 01:35: PM