Question

If α, β are roots of the equation x² + 5x + 5 = 0, then equation whose roots are α + 1 and β + 1 is:

Options

• x² + 5x – 5 = 0

• x² + 3x + 5 = 0

• x² + 3x + 1 = 0

• none of these

Answer 1

x² + 3x + 1 = 0

Explanation:

α + β = −5, αβ = 5

Required equation is

x² – (α + 1 + β + 1)x + (α + 1) (β + 1) = 0

⇒ x² – (α + β + 2)x + (αβ + α + β + 1) = 0

⇒ x² – (–5 + 2)x + (5 – 5 + 1) = 0

⇒ x² + 3x + 1 = 0