Using the given zero, find one other zero of f(x). If 1 - 6i is a zero of f(x) = x⁴ - 2x³ + 38x² - 2x + 37.

Solution:

We will use the complex conjugate root theorem, which states that if the polynomial has real coefficients then the complex zeroes of the polynomial occur in conjugate pairs.

Therefore, if 1 - 6i is a zero of polynomial f(x) = x⁴ - 2x³ + 38x² - 2x + 37.

The other zero is 1 + 6i.

Using the given zero, find one other zero of f(x). If 1 - 6i is a zero of f(x) = x⁴ - 2x³ + 38x² - 2x + 37.

Summary:

The zeroes of the polynomial f(x) = x⁴ - 2x³ + 38x² - 2x + 37 are 1 ± 6i.