If α,  β  are the roots of x2+px+q=0,  ω3=1,  then (ωα+ω2β). (ω2α+ωβ)=

The given equation is x2+px+q=0 α,  β  are the roots of given equationThen sum of the roots : α+β=−p,  Product of the roots : αβ=qNow (ωα+ω2β). (ω2α+ωβ)=α2(ω3)+(αβ)ω2+ω4(αβ)+ω3(β2)=(α2+β2)ω3+(αβ)ω2(1+ω2)=α2+β2−αβ(ω)3                 (∵  ω3=1,  1+ω+ω2=0)and subtract 2αβ=(α+β)2−3αβ=p2−3q