Question

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α²β + αβ²

Answer 1

f(x) = ax² + bx + c

α + β = `(-b/a)`

αβ = `c/a`

since α + β are the roots (or) zeroes of the given polynomials

then

α²β + αβ²

αβ(α + β)

`=c/a((-b)/a)`

`=(-bc)/a^2`