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Find the zeroes of the polynomial $p(x) = 3x^2 + x - 10$ and verify the relationship between zeroes and its coefficients.
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$p(x) = 3x^2 + x - 10 = (x + 2)(3x - 5)$
$\text{Zeroes of } p(x) \text{ are } -2 \text{ and } \frac{5}{3}$ (1 mark)
$\text{Sum of zeroes} = -2 + \frac{5}{3} = \frac{-1}{3} = -\frac{\text{coefficient of } x}{\text{coefficient of } x^2}$ (1 mark)
$\text{Product of zeroes} = -2 \times \frac{5}{3} = \frac{-10}{3} = \frac{\text{constant term}}{\text{coefficient of } x^2}$ (1 mark)
$\text{Zeroes of } p(x) \text{ are } -2 \text{ and } \frac{5}{3}$ (1 mark)
$\text{Sum of zeroes} = -2 + \frac{5}{3} = \frac{-1}{3} = -\frac{\text{coefficient of } x}{\text{coefficient of } x^2}$ (1 mark)
$\text{Product of zeroes} = -2 \times \frac{5}{3} = \frac{-10}{3} = \frac{\text{constant term}}{\text{coefficient of } x^2}$ (1 mark)