# How do you write a polynomial in standard form given zeros 5, -1, -3i, 3i?

May 1, 2016

${x}^{4} - 4 {x}^{3} + 4 {x}^{2} + 36 x - 45 = 0$.

#### Explanation:

The biquadratic equation is

$\prod \left(x - z e r o\right) = \left(x - 5\right) \left(x + 1\right) \left(x - 3 i\right) \left(x + 3 i\right) = 0$

So,$\left({x}^{2} - 4 x - 5\right) \left({x}^{2} + 9\right) = 0$, Expanding,
.
${x}^{4} - 4 {x}^{3} + 4 {x}^{2} + 36 x - 45 = 0$.