If  α,β,γ are the roots of x3+2x2−3x−1=0 , then α−2+β−2+γ−2=

The given equation is x3+2x2−3x−1=0  α,β,γ are the roots of given equation⇒s1=α+β+γ=−2, s2=αβ+βγ+γα=−3, s3=αβγ=1 ∴  α−2+β−2+γ−2=1α2+1β2+1γ2    =∑α2β2(αβγ)2  =∑(αβ)2−2αβγ∑α(αβγ)2  =(−3)2−2(1)(−2)(1)2   =13