Question

Find the quadratic polynomial whose sum and product of zeroes are √2 and 2+√2 respectively.

Answer 1

let , alpha and beta are the roots of quadratic equation.

therefore, required quadratic equation is ------- x^2 - ( alpha+ beta ) x + alpha × beta

therefore, x^2- root 2 x + 2 + root 2

Answer 2

$QE \: \: with \: roots \: \alpha \: \beta \: is \\ \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ given \\ \\ \alpha + \beta = \sqrt{2} \\ \\ \alpha \beta = 2 + \sqrt{2} \\ \\ = > {x}^{2} - \sqrt{2} x + (2 + \sqrt{2} ) = 0 \\ \\ is \: the \: required \: polynomial$

$\mathfrak{hope \: it \: helps} \\ \\ \bold{ Thank \: you}$