Given, α,β and γ are the roots of equation x3+4x2−9x−36=0 and α+β=0 ∴‌‌α+β+γ=−4⇒γ=−4 αβ+βγ+γα‌=−9 ⇒‌‌αβ+γ(α+β)‌=−9⇒αβ=−9 α(−α)‌=−9‌‌[∵α+β=0] −α2‌=−9⇒α2=3 If α=−3, then β=3 and if α=3, then β=−3 Now, α2+2β2+3γ2=9+2×9+3×16 =27+48=75