# How do you write a polynomial function of least degree given the zeros 0, 2, sqrt3?

##### 1 Answer
Aug 22, 2017

Polynomial function of least degree given zeros $0 , 2$ and $\sqrt{3}$ is ${x}^{3} - 2 {x}^{2} - \sqrt{3} {x}^{2} + 2 \sqrt{3} x$

#### Explanation:

A polynomial function of least degree given zeros $\alpha , \beta$ and $\gamma$ is

$\left(x - \alpha\right) \left(x - \beta\right) \left(x - \gamma\right)$

Hence, a polynomial function of least degree given zeros $0 , 2$ and $\sqrt{3}$ is

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

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

= ${x}^{3} - 2 {x}^{2} - \sqrt{3} {x}^{2} + 2 \sqrt{3} x$