# How do you write a polynomial function with minimum degree whose zeroes are -1, 2, 3i?

Mar 29, 2018

${x}^{4} - {x}^{3} + 7 {x}^{2} - 9 x - 18$

#### Explanation:

If $3 i$ is zero of this polynomial, $- 3 i$ is also zero of it. Hence

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

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

=$\left({x}^{2} - x - 2\right) \left({x}^{2} + 9\right)$

=${x}^{4} - {x}^{3} + 7 {x}^{2} - 9 x - 18$