Question

Find a quadratic polynomial whose zeroes are $3\pm \sqrt{2}$

Answer 1

Given zeros of polynomial are $3\pm \sqrt{2}$

Let $\alpha ,\beta$ be zeros of polynomial

then

$\alpha +\beta =3+\sqrt{2}+3-\sqrt{2}=6$ ________ (1)

& $\alpha \beta (3+\sqrt{2})(3-\sqrt{2})$

$\alpha \beta =9-3\sqrt{2}+3\sqrt{2}-2=7$ _________ (2)

then

quadratic equation is

$x^2-(\alpha +\beta )x+\alpha \beta =0$

From (1) & (2)

$[x^2-6x+7=0]$