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

According to the question,

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

Thus, p(x) = x^{3} – (α + β + γ )x^{2} + (αβ + βγ + γ α)x - αβγ

x^{3} – 3x^{2} – 10x + 24

Hence, option C is correct.

22