# How do you write a polynomial in standard form given the zeros 5 and 1+2i?

##### 1 Answer
Mar 26, 2018

${x}^{3} - 7 {x}^{2} + 15 x - 25$

#### Explanation:

If $1 + 2 i$ is root of a polynomial, $1 - 2 i$ also the root of it. Hence,

$P \left(x\right) = \left(x - 5\right) \left(x - 1 + 2 i\right) \left(x - 1 - 2 i\right)$

=$\left(x - 5\right) \left({x}^{2} - 2 x + 5\right)$

=${x}^{3} - 7 {x}^{2} + 15 x - 25$