Question

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

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

Answer 1

i got 2i, 7, -7

Answer 2

2i is a zero, means that (x - 2i) is a factor. Since complex roots always come in conjugate pairs, that means that (x + 2i) must also be a factor. So +2i and -2i are zeros.

(x + 2i)(x-2i) = x^2 -4i^2 = x^2 + 4

(x^4 - 45x^2 - 196)/(x^2 + 4) = x^2 - 49 and x^2 - 49 = (x + 7)(x - 7) so yes :D

7 and -7 are your other two roots. Good :D