# How do you find a polynomial function that has zeros x=0, sqrt3, -sqrt3 and degree n=3?

Sep 13, 2017

$p \left(x\right) = {x}^{3} - 3 x$

#### Explanation:

$\text{since the zeros are "x=0,x=sqrt3,x=-sqrt3" then}$

$\text{the factors are } x , \left(x - \sqrt{3}\right) , \left(x + \sqrt{3}\right)$

$\text{the polynomial is then the product of the factors}$

$\Rightarrow p \left(x\right) = x \left(x - \sqrt{3}\right) \left(x + \sqrt{3}\right)$

$\textcolor{w h i t e}{\Rightarrow p \left(x\right)} = x \left({x}^{2} - 3\right)$

$\textcolor{w h i t e}{\Rightarrow p \left(x\right)} = {x}^{3} - 3 x \leftarrow \text{ is a possible polynomial}$