Question

Pleaseeeee heeeelp write a polynomial function of least degree with the given zero. -1+ √ 2, √ 3

Answer 1

A polynomial $p(x)$ has a root $x_0$ if it is a multiple of $(x-x_0)$

So, if you want roots $-1, \sqrt{2}, \sqrt{3}$, your polynomial must be a multiple of

$(x+1)\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)$

If we add another monomial, we would raise the degree, but we want it to be as low as possible. So, we can only add a multiplicative constant: your polynomial is

$p(x)=a(x+1)\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)$