Question

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

• A. $-2,1,4$
• B. $0,2,4$
• C. $0,1,4$
• D. $-2,2,4$

Answer 1

Answer: (D)

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