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Find the zeroes of the polynomial $p(x) = 4x^2 - 4x - 3$ and verify the relationship between zeroes and its coefficients.
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$p(x) = 4x^2 - 4x - 3 = (2x + 1) (2x - 3)$
$\therefore$ zeroes of $p(x)$ are $-\frac{1}{2}$ and $\frac{3}{2}$ [$1$ mark]
Sum of zeroes $= -\frac{1}{2} + \frac{3}{2} = 1 = \frac{-(-4)}{4} = \frac{-\text{coefficient of } x}{\text{coefficient of } x^2}$ [$1$ mark]
Product of zeroes $= -\frac{1}{2} \times \frac{3}{2} = -\frac{3}{4} = \frac{\text{constant}}{\text{coefficient of } x^2}$ [$1$ mark]
$\therefore$ zeroes of $p(x)$ are $-\frac{1}{2}$ and $\frac{3}{2}$ [$1$ mark]
Sum of zeroes $= -\frac{1}{2} + \frac{3}{2} = 1 = \frac{-(-4)}{4} = \frac{-\text{coefficient of } x}{\text{coefficient of } x^2}$ [$1$ mark]
Product of zeroes $= -\frac{1}{2} \times \frac{3}{2} = -\frac{3}{4} = \frac{\text{constant}}{\text{coefficient of } x^2}$ [$1$ mark]