Given, α,β and gamma are roots of x3−3x2+x+5=0 ∴ α+β+γ=3 αβ+βγ+γα=1 αβγ=−5 Now, y=Σα2+αβγ y=(α2+β2+γ2)+αβγ y=(α+β+γ)2−2(αβ+βγ+yα)+αβγ y=(3)2−2(1)−5=9−7=2 ∴ y = 2 y=2 only satisficd the equation y3−y2−y−2=0