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?

1 Answer
Apr 16, 2018

(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.