Question

The sum and product of zeros of a quadratic polynomial are root 2 and1 upon 3nthe quadratic polynomial. Find the quadratic polynomial​

Answer 1

$let \: the \: zeros \: of \: polynomial \: be \: \alpha \: and \: \beta \\ \\ \alpha + \beta = \sqrt{2} \: (given) \\ \alpha \beta = \frac{1}{3} (given) \\ \\ quadratic \: polynomial \: form = \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = {x}^{2} \ - \sqrt{2} x + \frac{1}{3} \\ \\ = 3 {x}^{2} - 3 \sqrt{2} x + 1$

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