Question

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

(a) x³ + 3x² – 10x + 24 

(b) x³ + 3x² + 10x – 24 

(c) x³ – 3x² – 10x + 24

(d) none of these

Answer 1

(c) x³ – 3x² – 10x + 24 

Given: 

α, β and γ are the zeroes of polynomial p(x). 

Also, (α + β + γ) = 3, (αβ + βγ + γα) = –10 and αβγ = –24 

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

= x³ – 3x² – 10x + 24