Question:
For the equation $|x|^{2}+|x|-6=0$, the sum of the real roots is
(a) 1
(b) 0
(c) 2
(d) none of these
Solution:
(b) 0
Let $p=|x|$
$\Rightarrow p^{2}+p-6=0$
$\Rightarrow p^{2}+3 p-2 p-6=0$
$\Rightarrow(p+3)(p-2)=0$
$\Rightarrow p=-3,2$
Also, $|x|=p$
$\Rightarrow|x|=2$, or $|x|=-3$
Modulus can not be negative,$\therefore|x|=2$
$\Rightarrow x=\pm 2$
$\Rightarrow x=2$ or $-2$
Sum of the roots of $x$ is 0