The product of the distinct roots of | Quantitative Aptitude – Algebra – Quadratic equations

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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Algebra – Quadratic Equations – The product of the distinct roots of…

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2019 – Slot -1 - Question 3 - The product of the distinct roots of...

Q. 3: The product of the distinct roots of ∣x^2 − x − 6∣ = x + 2 is?

1. −16
2. -8
3. -24
4. -4

Show Answer

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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