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Find the zeroes of the polynomial $4x^2 + 4x + 1$ and verify the relationship between the zeroes and the coefficients of the given polynomial.
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$4x^2 + 4x + 1$
$(2x + 1)(2x + 1)$
Zeroes are $-\frac{1}{2}$ and $-\frac{1}{2}$ [$1$ mark]
Sum of zeroes $= -\frac{1}{2} + (-\frac{1}{2}) = -1 = \frac{-4}{4} = \frac{-\text{Coefficient of } x}{\text{Coefficient of } x^2}$ [$1$ mark]
Product of zeroes $= -\frac{1}{2} \times -\frac{1}{2} = \frac{1}{4} = \frac{\text{constant term}}{\text{Coefficient of } x^2}$ [$1$ mark]
$(2x + 1)(2x + 1)$
Zeroes are $-\frac{1}{2}$ and $-\frac{1}{2}$ [$1$ mark]
Sum of zeroes $= -\frac{1}{2} + (-\frac{1}{2}) = -1 = \frac{-4}{4} = \frac{-\text{Coefficient of } x}{\text{Coefficient of } x^2}$ [$1$ mark]
Product of zeroes $= -\frac{1}{2} \times -\frac{1}{2} = \frac{1}{4} = \frac{\text{constant term}}{\text{Coefficient of } x^2}$ [$1$ mark]