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Q. The roots of the equation $\left |x^{2}-x-6\right|=x+2$ are

AP EAMCETAP EAMCET 2020

Solution:

Given, $\left |x^{2}-x-6\right|=x+2$
$\Rightarrow x^{2}-x-6=x+2$
Or $x^{2}-x-6=-x-2$
$\Rightarrow x^{2}-2 x-8=0$ or $x^{2}=4$
$\Rightarrow (x=-2,4)$ or $(x=\pm 2)$
$\Rightarrow x=\{-2,2,4\}$