# How do you find a polynomial function with zeroes 2, -6, and 2+ 4i?

##### 1 Answer
Jun 8, 2015

If you would like the polynomial to have real coefficients, then the simplest one is:

$f \left(x\right) = \left(x - 2\right) \left(x + 6\right) \left(x - 2 - 4 i\right) \left(x - 2 + 4 i\right)$

$= \left({x}^{2} + 4 x - 12\right) \left({x}^{2} - 4 x + 20\right)$

$= {x}^{4} - 8 {x}^{2} + 128 x - 240$