If \( \alpha \) and \( \beta \) are the zeros of the quadratic poly...

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If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \( f(x)=x^{2}-p x+q \), prove that
\[
\frac{\alpha^{2}}{\beta^{2}}+\frac{\beta^{2}}{\alpha^{2}}=\frac{p^{4}}{q^{2}}-\frac{4 p^{2}}{q}+2
\]
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