Question

If α and β are the zeros of the quadratic polynomial f(x) = x² - px + q,

prove that \(\frac{\alpha^2}{\beta^2}\) + \(\frac{\beta^2}{\alpha^2}\) = \(\frac{p^4}{q^2}\) - \(\frac{4p^2}{q}\) + 2

Answer 1

Let one root of the given quadratic polynomial is α

Other root of the given quadratic polynomial is β

Sum of the roots

Product of the roots

Therefore, we have

Hence, Proved.