Question

If α and β are the zeros of the quadratic polynomial p(x) = 4x² – 5x – 1, find the value of α²β + αβ².

Answer 1

Since α and β are the roots of the polynomial: 4x² – 5x – 1

∴ Sum of the roots `alpha+beta=5/4`

Product of the roots `alphabeta=(-1)/4`

Hence `alpha^2beta+alphabeta^2=alphabeta(alpha+beta)=5/4((-1)/4)=(-5)/16`