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# Using the given zero, find one other zero of f(x). If 1 - 6i is a zero of f(x) = x^{4} - 2x^{3} + 38x^{2} - 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) = x^{4} - 2x^{3} + 38x^{2} - 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) = x^{4} - 2x^{3} + 38x^{2} - 2x + 37.

**Summary:**

The zeroes of the polynomial f(x) = x^{4} - 2x^{3} + 38x^{2} - 2x + 37 are 1 ± 6i.

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