If α and β are the zeros of the quadratic polynomial f(x) = x2 − px + q, prove that α2β2+β2α2=p2q2-4p2q+2.

If α and β are the zeros of the quadratic polynomial f(x) = x2 − p

1.	If α and β are the zeros of the quadratic polynomial f(x) = x2 − px + q, prove that α2β2+β2α2=p2q2-4p2q+2.
Answer» If α and β are the zeros of the quadratic polynomial f(x) = x² − px + q, prove that $\frac{α^{2}}{β^{2}} + \frac{β^{2}}{α^{2}} = \frac{p^{2}}{q^{2}} - \frac{4 p^{2}}{q} + 2$ .

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If α and β are the zeros of the quadratic polynomial f(x) = x2 − px + q, prove that α2β2+β2α2=p2q2-4p2q+2.

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