Question

if alpha and beta are the zeros of the quadratic polynomial ax square + bx + c then evaluate Alpha square + beta square

Answer 1

If α and β are the zeros of polynomial p(x)=ax²+bx+c
then, α+β=$\frac{-b}{a}$
and  αβ=$\frac{c}{a}$

α²+β²=(α+β)²-2αβ
α²+β²=$(\frac{-b}{a} )^{2}$-2$\frac{c}{a}$
α²+β²=$\frac{b^2}{a^2}$ - 2$\frac{c}{a}$