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Form a quadratic polynomial whose sum and product of the zeroes are $\frac{1}{2}$ and $-\frac{1}{2}$ respectively. Hence, find the zeroes of the polynomial.
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Solution: (a) Required polynomial is $k(x^2 - \frac{1}{2}x - \frac{1}{2})$ or $18x^2 - 9x - 2$ (1 Mark)
Zeroes of the polynomial are $-\frac{1}{6}$ and $\frac{2}{3}$ (1 Mark)
Zeroes of the polynomial are $-\frac{1}{6}$ and $\frac{2}{3}$ (1 Mark)