Question

Find a polynomial function of lowest degree with

rational coefficients that has the given numbers
as some of its zeros.
- 5i, 4

Answer 1

x^3-4x^2+25x-100

Explanation:

We have 2 roots -5i and 4. Using the conjugate root theorem for the root -5i, we know that 5i should be another root

Combining the roots into a polynomial gives us:

(x+5i)(x-5i)(x-4)

Expand:

(x^2 + 25)(x-4)

x^3-4x^2+25x-100