Let α, β and γ be the roots of the equation x^3+x+1=0, then (αβα+β+βγβ+γ+γαγ+α)/(α^2+β^2+γ^2) is equal to

Question

MARKS Content Team · Accepted Answer

Correct answer: (D) -3/2. α+β+γ=0,∑αβ=1,αβγ=-1 ∑αβα+β=∑αβ-γ=-3αβγ=3 α^2+β^2+γ^2=α+β+γ^2-2αβ+βγ+γα=-2 Hence, (∑αβα+β)/(α^2+β^2+γ^2)=-3/2

Let $α, β$ and $γ$ be the roots of the equation $x^{3} + x + 1 = 0,$ then $\frac{α β (α + β) + β γ (β + γ) + γ α (γ + α)}{α^{2} + β^{2} + γ^{2}}$ is equal to