Question

If α and β are the zeros of the quadratic polynomial f(x) = x² − px + q, prove that $\frac{{\mathrm{\alpha }}^2}{{\mathrm{\beta }}^2}+\frac{{\mathrm{\beta }}^2}{{\mathrm{\alpha }}^2}=\frac{p^2}{q^2}-\frac{4p^2}{q}+2$.

Answer 1

Since and are the zeros of the quadratic polynomial

= p

We have,

Hence, it is proved that is equal to .