Using the given zero, find one other zero of f (x). Explain the process you used to find your solution.

2 - 3i is a zero of f (x) = x4 - 4x3 + 14x2 - 4x + 13.

Complex zeroes always occurs as conjugates.

For z = a + b i conjugate is: a - b i

Another zero is : 2 + 3 i.

Verification:

2 + 3 i + 3 - 3 i = - b/a

- b = 4, a = 1

(2 + 3 i) (2 - 3 i) = c / a

4 - 9 i² = c / a

4 + 9 = c / a

c = 13

(x^4 - 4 x³ + 14 x² - 4 x + 13) : (x² - 4 x + 13) = x² + 1

x² + 1 = 0

x² = - 1, x = i, x = - i

The zeroes are: - i, i, 2 + 3 i, 2 - 3 i.

Answer:

One another zero of f (x) is 2 + 3 i.