# How do you find a polynomial function with zeroes 2, -4, -3i?

Oct 23, 2015

${x}^{3} + \left(2 + 3 i\right) x + \left(- 8 + 6 i\right) x - 24 i$

#### Explanation:

If the three roots are given, then we may obtain the corresponding 3 factors and hence write the polynomial as

$\left(x - 2\right) \left(x + 4\right) \left(x + 3 i\right) = 0$

Multiplying this out you will get the polynomial with complex coefficients in standard form

${x}^{3} + \left(2 + 3 i\right) x + \left(- 8 + 6 i\right) x - 24 i$