Question

find the quadratic polynomial each
e
the
Zereos
sum and product of its
respectively
are
$\sqrt{2}$
and 1by3

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Answer 1

$let \: the \: zeroes \: be \: \alpha \: and \: \beta . \\ acc \: to \: ques \\ \alpha + \beta = \sqrt{2} \\ \alpha \beta = \frac{1}{3} \\ then \: polynomial \: = {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ = > {x}^{2} - \sqrt{2} x + \frac{1}{3} = 0 \\ = > 3 {x}^{2} - 3 \sqrt{2} x + 1 = 0$