# How do you write a polynomial in standard form given zeros 1 and 2 + 3i?

Jul 15, 2016

${x}^{2} - \left(3 + 3 i\right) x + \left(2 + 3 i\right)$

#### Explanation:

A zero, say $a$ of a polynomial $f \left(x\right)$ is one for which $f \left(a\right) = 0$.

Let us assume that zeros are $\left\{a , b , c , d\right\}$, then it is apparent that such a polynomial could be $\left(x - a\right) \left(x - b\right) \left(x - c\right) \left(x - d\right)$.

As we need to write a polynomial with zeros $1$ and $2 + 3 i$, the polynomial is

$\left(x - 1\right) \left(x - 2 - 3 i\right)$ or

$x \left(x - 2 - 3 i\right) - 1 \left(x - 2 - 3 i\right)$ or

${x}^{2} - 2 x - 3 i x - x + 2 + 3 i$ or

${x}^{2} - 3 x - 3 i x + 2 + 3 i$ or

${x}^{2} - \left(3 + 3 i\right) x + \left(2 + 3 i\right)$