Question

Using the given zero, find all other zeros of f(x).

-2i is a zero of f(x) = x^4 - 45x^2 - 196

2i, 14i, -14i

2i, 7, -7

2i, 14, -14

2i, 7i, -7i

Answer 1

Are you familiar with either (1) synthetic division or (2) long division?

Answer 2

I know long division

Answer 3

In that case, take the given zero, -2i, and convert that to a factor, (x+2i).
Now use long division to divide that into the given polynomial.

Answer 4

Makes the division a bit more complicated, but otherwise, no. Recall that i^2=-1. Have you seen that before?

Answer 5

I think so yes

Answer 6

Good. Then set up the necessary long division: divide (x+2i) into x^4 - 45x^2 - 196.

Answer 7

I'm getting some strange numbers. Can you walk me through the first set so I know I'm doing the math right?

Answer 8

I'm trying the same problem myself, and am not yet satisfied with my own work. What do you mean by "strange numbers"? There's no way to avoid getting that "i" in some of your terms.

Answer 9

I know I can't get rid of that i, but I'm getting numbers that don't look like they belong there

Answer 10

could you possibly share a screen shot of your work, or a photo?