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Find the zeroes of the polynomial $2x^2 + 7x + 5$ and verify the relationship between its zeroes and co-efficients.
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$p(x) = 2x^2 + 7x + 5 = (x + 1)(2x + 5)$
Zeroes of $p(x)$ are $-1$ and $-\frac{5}{2}$
Sum of zeroes $= -1 - \frac{5}{2} = -\frac{7}{2} = -\frac{\text{coefficient of } x}{\text{coefficient of } x^2}$
Product of zeroes $= (-1)(-\frac{5}{2}) = \frac{5}{2} = \frac{\text{constant term}}{\text{coefficient of } x^2}$
Zeroes of $p(x)$ are $-1$ and $-\frac{5}{2}$
Sum of zeroes $= -1 - \frac{5}{2} = -\frac{7}{2} = -\frac{\text{coefficient of } x}{\text{coefficient of } x^2}$
Product of zeroes $= (-1)(-\frac{5}{2}) = \frac{5}{2} = \frac{\text{constant term}}{\text{coefficient of } x^2}$