Question

Find the product of distinct roots of ∣X² – 2X - 15∣ = X + 3

1. 28
2. -28
3. -72
4. 72

Answer 1

Correct Answer - Option 3 : -72

Calculation:

Case 1: X² – 2X - 15 = X + 3

⇒ X² – 3X - 18 = 0

⇒ X² – 6X + 3X - 18 = 0

⇒ (X – 6)(X + 3) = 0

∴ x = 6, -3

Case 2: X² – 2X - 15 = -X - 3

⇒ X² – X - 12 = 0

⇒ X² – 4X + 3X - 12 = 0

⇒ (X – 4)(X + 3) = 0

⇒ X = 4, - 3

Product of all possible distinct roots = 4 × -3 × 6

⇒ -72

∴ required answer is -72

Two possibilities arise in case of modulus

Eg: ∣x ∣ = 3

Case 1: X = +3

Case 2: X = -3