The roots of the equation is α and β . So, α+β=4 αβ=5 Now, (α2+β)+(α+β2)=(α+β)2−2αβ+(α+β) =16−10+4 =10 And (α2+β)+(α+β2)=α3+α2β2+βα+β3 =α3+β3+αβ(αβ+1) =(α+β)[(α+β)2−3αβ]+αβ(αβ+1) =4[16−15]+5(6) = 34 So, the quadratic equation whose roots are (α2+β) and (α+β2) is x2−(α2+β+α+β2)x+(α2+β)(α+β2)=0 x2−10x+34=0