Question

If α + β = 4 and α³ + β³ = 44, then α, β are the roots of the equation:

Options

• 2x² – 7x – 7 = 0

• 3x² + 8x + 12 = 0

• 3x² – 12x + 5 = 0

• none of these

Answer 1

3x² – 12x + 5 = 0

Explanation:

α³ + β³ = (α + β)³ – 3αβ(α + β)

⇒ 44 = (4)³ – 3αβ × 4

⇒ 44 – 64 = – 12 αβ

⇒ αβ = `20/12 = 5/3`

∴ quadratic equation is

x² – (α + β)x + αβ = 0

⇒ x² – 4x + 53 = 0

⇒ 3x² – 12x + 5 = 0