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

Sep 1, 2016

The desired polynomial is
${x}^{2} + \left(1 - 2 i\right) x - 2 - 4 i$

#### Explanation:

If $a$, $b$ and $c$ are the zeros of a polynomial, then the polynomial is

$\left(x - a\right) \left(x - b\right) \left(x - c\right)$.

Hence, the polynomial with zeros as $- 2$ and $1 + 2 i$ will be

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

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

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

${x}^{2} - x - 2 i x + 2 x - 2 - 4 i$ or

${x}^{2} + x - 2 i x - 2 - 4 i$ or

${x}^{2} + \left(1 - 2 i\right) x - 2 - 4 i$