Without actually calculating the zeroes, form a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial $5x^2 + 2x - 3$.

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Step 1: Let zeroes of given quadratic polynomial be $\alpha$ and $\beta$. $\alpha + \beta = \frac{-2}{5}$ and $\alpha\beta = \frac{-3}{5}$
Step 2: Now, $\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\beta + \alpha}{\alpha\beta} = \frac{\frac{-2}{5}}{\frac{-3}{5}} = \frac{2}{3}$
Step 3: $\frac{1}{\alpha\beta} = \frac{-5}{3}$
Step 4: Required Polynomial is $x^2 - \frac{2}{3}x - \frac{5}{3}$ or $3x^2 - 2x - 5$

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