Question

If α, β, γ be the zeros of the polynomial p(x) such that (α + β + γ) = 3, (αβ + βγ + γα) = –10 and αβγ = –24 then p(x) = ?

Options

• x³ + 3x² – 10x + 24

• x³ + 3x² + 10x – 24

• x³ – 3x² – 10x + 24

• None of these

Answer 1

x³ – 3x² – 10x + 24

Explanation:

p(x) = x³ – (α + β + γ)x² + (αβ + βγ + γα)x – αβγ

= x³ – 3x² – 10x + 24