# How do you write a polynomial with zeros 2,-2,-6i?

Feb 20, 2016

Polynomial is ${x}^{3} + 6 i {x}^{2} - 4 x - 24 i$

#### Explanation:

A polynomial with zeros as $a , b , c$ is $\left(x - a\right) \left(x - b\right) \left(x - c\right)$, as each of $a , b , c$ make the vale of polynomial zero

Hence, A polynomial with zeros as $2 , - 2 , - 6 i$ is

$\left(x - 2\right) \left(x - \left(- 2\right)\right) \left(x - \left(- 6 i\right)\right)$ i.e.

$\left(x - 2\right) \left(x + 2\right) \left(x + 6 i\right)$ or

$\left({x}^{2} - 4\right) \left(x + 6 i\right)$ or

${x}^{3} + 6 i {x}^{2} - 4 x - 24 i$