If α, β are the roots of x2−px+q=0 and α′, β′ are the roots of x2−p′x+q′=0 then the value of α−α′2+β−α′2+α−β′2+β−β′2 is

Since α, β are the roots of x2−px+q=0and α′, β′ are the roots of x2−p′x+q′=0α+β=p,αβ=q,α′+β′=p′,α′β′=q′Now, α−α′2+β−α′2+α−β′2+β−β′2=2α2+β2+2α′2+β′2−2α′(α+β)−2β′(α+β)=2(α+β)2−2αβ+α′+β′2−2α′β′−(α+β)α′+β′=2p2−2q+p′2−2q′−pp′