Question

WILL GIVE MEDAL!!! 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.

Answer 1

If a - ib is a zero then a+ib is a zero

Answer 2

So
1+ 6i
is a zero

Answer 3

Here are the four roots
(i, -i, 1+ 6i, 1-6i)

Answer 4

Is that everytime though?

Answer 5

Yes, when the polynomial has rational coefficients

Answer 6

That makes sense. Thank you!

Answer 7

YW

Answer 8

\[
x^4 - 2 x^3 + 38 x^2 - 2 x + 37 = (1 + x^2) (37 - 2 x + x^2)=0
\]
When you use the quadratic formula, then\[x= something \pm i \quad somethingelse\]