# How do you write a polynomial in standard form given zeros 5i and -5i?

Apr 15, 2016

#### Answer:

${x}^{2} + 25$

#### Explanation:

If $\textcolor{red}{5 i}$ and $\textcolor{b l u e}{- 5 i}$ are zeros of a polynomial
then
$\textcolor{w h i t e}{\text{XXX}} \left(x - \textcolor{red}{5 i}\right)$ and $\left(x \textcolor{b l u e}{+ 5 i}\right)$ are factors of that polynomial.

The simplest polynomial with these factors will be the product of these (and only these) factors:
$\textcolor{w h i t e}{\text{XXX}} \left(x - 5 i\right) \left(x + 5 i\right) = {x}^{2} + 25$