Question

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

-2. 3i , and 5

Answer 1

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

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.