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Find the zeroes of the polynomial $4x^2 + 4x - 3$ and verify the relationship between zeroes and coefficients of the polynomial.
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$$\begin{aligned}& P(x) = 4x^2 + 4x - 3 \\ & = (2x + 3) (2x - 1) \\ & \therefore \text{Zeroes of the polynomial are } -\frac{3}{2}, \frac{1}{2} \\ & \text{Sum of Zeroes } = -\frac{3}{2} + \frac{1}{2} = \frac{-3+1}{2} = \frac{-4}{4} = -1 = -\frac{(\text{coefficient of } x)}{(\text{coefficient of } x^2)} \\ & \text{Product of Zeroes } = -\frac{3}{2} \times \frac{1}{2} = -\frac{3}{4} = \frac{\text{constant term}}{(\text{coefficient of } x^2)}\end{aligned}$$