# How do you write a polynomial equation of least degree given the roots -5i, -i, i, 5i?

Jan 15, 2017

${x}^{4} + 26 {x}^{2} + 25 = 0$

#### Explanation:

Each zero $a$ corresponds to a factor $\left(x - a\right)$.

So we can write:

$f \left(x\right) = \left(x - 5 i\right) \left(x + 5 i\right) \left(x - i\right) \left(x + i\right)$

$\textcolor{w h i t e}{f \left(x\right)} = \left({x}^{2} + 25\right) \left({x}^{2} + 1\right)$

$\textcolor{w h i t e}{f \left(x\right)} = {x}^{4} + 26 {x}^{2} + 25$

So a suitable polynomial equation is:

${x}^{4} + 26 {x}^{2} + 25 = 0$