# How do you write a polynomial with roots – square root of 3 , square root of 3 , and 2 ?

Jan 14, 2016

$y = {x}^{3} - 2 {x}^{2} - 3 x + 6$

#### Explanation:

Note that if a polynomial has root $b$, then the binomial $\left(x - b\right)$ is a factor of the polynomial.

Thus, since the roots are $- \sqrt{3} , \sqrt{3} , 2$, the polynomial can be expressed as

$y = \left(x - \left(- \sqrt{3}\right)\right) \left(x - \sqrt{3}\right) \left(x - 2\right)$
$= \left(x + \sqrt{3}\right) \left(x - \sqrt{3}\right) \left(x - 2\right)$
$= \left({x}^{2} - 3\right) \left(x - 2\right)$
$= {x}^{3} - 2 {x}^{2} - 3 x + 6$