Given, α,β,γ are roots of x3−2x2+3x−4=0 ∴‌‌α+β+γ=2 αβ+βγ+γα=−3 αβγ=4 , We can simplify the expression αβ(α+β)+βγ(β+γ)+γα(γ+α) as follows: αβ(α+β)+βγ(β+γ)+γα(γ+α) =α2β+β2γ+γ2α+αβ2+βγ2+γα2 =(α+β+γ)(αβ+βγ+γα) =2⋅3=6