Question

The sum of all real roots of the equation ${\left|x-2\right|}^2+\left|x-2\right|-2=0$ is

• A. $7$
• B. $4$
• C. $1$
• D. $5$

Answer 1

Answer: (B)

Given, ${\left|x-2\right|}^2+\left|x-2\right|-2=0$
$\therefore y^2+y-2=0$, where $y=\left|x-2\right|$
$\Rightarrow \left(y+2\right)\left(y-1\right)=0$
$y=1[\because y=\left|x-2\right|=-2$ not possible]
$\Rightarrow \left|x-2\right|=1$
$\Rightarrow x-2=\pm 1$
$\Rightarrow x=3,1$
$\therefore$ Sum of roots is $4$