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

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

Question

Using the given zero, find one other zero of f(x). Explain the process you used to find your solution.

1 - 6i is a zero of f(x) = x4 - 2x3 + 38x2 - 2x + 37.

anonymous · Answer

I need help, I don't understand what exactly I'm suppose to do.

primeralph · Answer

if 1-6i is a zero, then 1+6i is a zero. Find the quadratic equation that has roots 1-6i and 1+6i. That quadratic is a factor of f(x). Find the other factors.

In this case, you're asked to find only one other zero, not all zeros, so your answer is 1+6i. The reason is that complex roots of real polynomials occur as conjugates: a+bi and a-bi.

anonymous · Answer

Thank you! I now I see what you mean, I get it. (:

primeralph · Answer

You're welcome.