Question

How do you write a polynomial function of least degree that has real coefficients, the following given zeros -2,-2,3,-4i and a leading coefficient of 1?

Answer 1

`(x+2)^2(x-(3-4i))(x+(3-4i))`

Explanation:

-2 has a multiplicity of 2 so you can start out with `(x+2)^2` and since `3-4i` is a zero you can multiply it, so: `(x+2)^2(x-(3-4i))` and if you need real coefficients the other zero would have to be `3+4i` because this is the only way to eliminate the `i` in this function so, `(x+2)^2(x-(3-4i))(x+(3-4i))`
Then expand if you need to.