# The sum of all real roots of the equation: $|x-2|^2+|x-2|-2=0$ is ?

$\begin{array}{1 1}(A) \;7\\(B)\;5\\(C)\;4 \\(D)\;1 \end{array}$

Given eqn.: $|x-2|^2+|x-2|-2=0$
Let $|x-2|=y$
$\Rightarrow\:y^2+y-2=0$
$\Rightarrow\:y=-2 \:\:or\:\:1$
$\Rightarrow\:|x-2|=-2,\:or\:1$
Since the roots are real, $|x-2|=1$
$\Rightarrow\:x=1\:\:or\:\:3$
sum of the roots$=3+1=4$
answered Jul 17, 2013