cat 2019 Question 7

Question

The product of the distinct roots of $\mid x^2 - x - 6 \mid = x + 2$ is

Accepted Answer

We have, $\mid x^2 - x - 6 \mid = x + 2$

=> |(x-3)(x+2)|=x+2

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

=> x - 3 = 1 => x = 4 (Rejected as x<-2)

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

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

Hence the product =4*-2*2=-16

Question 7.