If α,β,γ  are the roots of x3−x2+8x−6=0, then(1+α)(1+β)(1+γ)=

The given equation is x3−x2+8x−6=0, α,β,γ  are the roots of the equationSum of the roots : α+β+γ=1 Sum of the product of two roots taken two at a time  : αβ+βγ+γα=8 Product of the roots : αβγ=6 ∴(1+α)(1+β)(1+γ)=1+∑α+∑αβ+αβγ                            (∵(1+a)(1+b)(1+c)=1+(a+b+c)+(ab+bc+ca)+(abc) )                                           =1+1+8+6                                              =16