If α  and  β are the roots of the equation ax2+bx+c=0; (a, b, c∈R)  then (1+α+α2)(1+β+β2)  is

The given equation is ax2+bx+c=0 α  and  β are the roots of the equationSum of the roots: α+β=−ba,   Product of the roots αβ=ca  (1+α+α2)(1+β+β2) =1+(α+β)+(α2+β2)+αβ+αβ(α+β)+α2β2 =1+(α+β)+(α+β)2−αβ+αβ(α+β)+(αβ)2 =1−b/a+b2/a2−c/a+(c/a)(−b/a)+c2/a2 =(a2+b2+c2−ab−bc−ca)a2 =[(a−b)2+(b−c)2+(c−a)2](2a2) which is positive