Question

find a quadratic polynomial whose zeroes are -1/2 and 2/3.

Answer 1

$zeroes \: are \: - \frac{ - 1}{2} and \: \frac{2}{3 } \\ sum \: of \: zeroes \: = \frac{ - 1}{2 } + \frac{2}{3 } \\ = \frac{ - 1 \times 3 + 2 \times 2 }{6} \\ = \frac{ - 3 + 4}{6} \\ = \frac{1}{6} \\ product \: ofzeroes = \frac{ - 1}{2} \times \frac{2}{3} \\ = \frac{ - 2}{6} \\ = \frac{ - 1}{3} \\ \\ now \: the \: polynomal \: is \\ {x}^{2} - (sum \: of \: zeroes)x + \\ product \: of \: zeroes \\ = {x}^{2} - \frac{1}{6} x - \frac{1}{3}$

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