Find a quadratic polynomial with zeroes

Given that the zeroes of the quadratic polynomial are $3+\sqrt{2}$ and $3-\sqrt{2}$.

We have to find the quadratic polynomial from the given zeroes.

Let we assume that,

$\alpha=3+\sqrt{2}$

$\beta=3-\sqrt{2}$, then

$\alpha+\beta=3+\sqrt{2}+3-\sqrt{2}$

$=6$

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

$=7$

Therefore the quadratic equation is given by

$x^{2}-(\alpha+\beta) x+\alpha \beta=x^{2}-6 x+7$

Hence the desire polynomial is $x^{2}-6 x+7$