$\alpha$ and $\beta$ are zeroes of a quadratic polynomial $px^2 + qx + 1$. Form a quadratic polynomial whose zeroes are $\frac{2}{\alpha}$ and $\frac{2}{\beta}$.

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Step 1: $\alpha + \beta = -\frac{q}{p}$, $\alpha\beta = \frac{1}{p}$
Step 2: Sum of new zeroes $= \frac{2}{\alpha} + \frac{2}{\beta} = \frac{2(\alpha + \beta)}{\alpha\beta} = \frac{2(-q/p)}{1/p} = -2q$
Step 3: Product of new zeroes $= \frac{4}{\alpha\beta} = \frac{4}{1/p} = 4p$
Step 4: $	herefore$ Required polynomial is $x^2 + 2qx + 4p$.

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