Question

find a quadratic polynomial each with the given number as the sum and product of zeros respectively root 2 ,1 upon 3 ​

Answer 1

$\huge\bf\blue{Hey\:Mate!!!}$

We are given that

Sum of zeroes= $\sqrt{2}$

Product of zeroes = $\frac{1}{3}$

Therefore the polynomial will be

$k( {x}^{2} - (sum \: of \: zeroes)x + (product \:o f \: zeroes)) \\ \\ p(x) = k( {x}^{2} - \sqrt{2} + \frac{1}{3} ) \\ \\ p(x) = k( \frac{3 {x}^{2} - 3 \sqrt{2} + 1}{3} ) \\ \\ for \: k = 3 \\ \\ p(x) = 3 {x}^{2} - 3 \sqrt{2} + 1$

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@ItsMysteriousGirl✒️