CAT 2019

Slot 1

QA

Question & Solution

We have, $|x^2 - x - 6| = x + 2$

$\Rightarrow |(x-3)(x+2)| = x+2$

For $x < -2$, $(3-x)(-x-2) = x+2$

$\Rightarrow x-3=1 \Rightarrow x=4$ (Rejected as $x < -2$)

For $-2 \le x < 3$, $(3-x)(x+2) = x+2 \Rightarrow x=2, -2$

For $x \ge 3$, $(x-3)(x+2) = x+2 \Rightarrow x=4$

Hence the product = $4 \times -2 \times 2 = -16$