If alpha and beta are the roots of 5x2 − 9x − 4 = 0, find the equation whose roots are (alpha2 - 3) and (beta2 - 3).

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9. PURE MATHEMATICS

a) If $\alpha$ and $\beta$ are the roots of $5x^2 - 9x - 4 = 0$, find the equation whose roots are $(\alpha^2 - 3)$ and $(\beta^2 - 3)$.

Step 1: Find the sum and product of the roots of the original equation $5x^2 - 9x - 4 = 0$.
For a quadratic equation $ax^2 + bx + c = 0$, the sum of roots is $\alpha + \beta = -\frac{b}{a}$ and the product of roots is $\alpha\beta = \frac{c}{a