If α,β,γ are the roots of  x3+2x2+3x+8=0, then(α+β)(β+γ)(γ+α)=

The given equation is x3+2x2+3x+8=0  α,β,γ  are the roots of the equationSum of the roots : α+β+γ=−2 Sum of the product of two roots taken two at a time  : αβ+βγ+γα=3 Product of the roots : αβγ=−8 Now(α+β)(β+γ)(γ+α)=(α+β+γ−γ)(β+γ+α−α)(γ+α+β−β)                                                         =(−2−γ)(−2−α)(−2−β)   (∵α+β+γ=−2)                                                     =−[8+4(α+β+γ)+2(αβ+βγ+γα)+αβγ]                                                     =−[8+4(−2)+2(3)+(−8)]                                                     =−[−2]=2 ∴(α+β)(β+γ)(γ+α)=2