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Q.
For the equation $\left|x^{2}\right|+|x|-6=0$, the roots are
Complex Numbers and Quadratic Equations
Solution:
For, $x<0,|x|=-x$
$\therefore $ equation is
$x^{2}-x-6=0 $
$\Rightarrow x=-2,3$
$\because x< 0$
$\therefore x=-2$ is the solution
For, $x \geq 0,|x|=x$,
$\therefore $ equation is
$x^{2}+x-6=0 $
$\Rightarrow x=2,-3$
$\because x \geq 0$
$\therefore x=2$ is the solution.
Hence, $x=2,-2$ are the solutions and their sum is zero.