Q. 3: The product of the distinct roots of ∣x^2 − x − 6∣ = x + 2 is?
1. −16
2. -8
3. -24
4. -4
given, ∣x^2 − x − 6∣ = x + 2
Or I (x-3)*(x+2)I = (x+2)
Case 1) When x > 3
Then (x-3)*(x+2)= (x+2) or x -3 =1 or x = 4
Case 2) when – 2 <= x < 3, -(x-3)*(x+2)= (x+2)
-(x-3)*(x+2) – (x+2) =0
(x+2)(x-3+1) =0
(x-2)*(x+2) =0
x = 2 or -2
case 3 ) when x < – 2
(x-3)*(x+2) = (x+2)
x = 4 (not possible as x < -2
so required product = 4*2*(-2) = -16
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