Question

Using the given zero, find one other zero of f(x). Explain the process you used to find your solution.
1 - 2i is a zero of f(x) = x4 - 2x3 + 6x2 - 2x + 5.

Answer 1

By the complex conjugate root theorem:

Since 1 - 2i is a zero of the function and since each term has real coefficients, then the conjugate of 1 - 2i must be a zero as well.

Answer 2

thanks @zpupster