the sum of the roots of the equation |x-2|^2 +|x-2|-2=0 is

 

Asked by amarnath3473 | 13th Jun, 2021, 12:43: PM

Expert Answer:

When x > 2, we have
(x - 2)2 + x - 2 - 2 = 0
x2 - 4x + 4 + x - 4 = 0
x2 - 3x = 0
x = 0 or x = 3
 
When x < 2. we have
-(x - 2)2 - x + 2 - 2 = 0
-x2 + 4x - 4 - x = 0
-x2 + 3x - 4 = 0
x2 - 3x + 4 = 0
We get non-real roots.
Therefore, x = 0 or 3
Sum of the roots = 3

Answered by Renu Varma | 14th Jun, 2021, 10:47: AM

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