Write an equation for a polynomial function that has the given roots

-2. 3i, and 5

x^4 - 3x^3 - x^2 - 27x - 90 = 0.

Step-by-step explanation:

If 3i is one root then another is - 3i.

In factor form we have:

(x + 2) (x - 5) (x - 3i) (x + 3i) = 0

(x^2 - 3x - 10) (x^2 - 9i^2) = 0

(x^2 - 3x - 10) (x^2 + 9) = 0

x^4 + 9x^2 - 3x^3 - 27x - 10x^2 - 90 = 0

x^4 - 3x^3 - x^2 - 27x - 90 = 0.