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

The imaginary zeros come in conjugate pairs, so -2i and 2i are zeros. To be zeros, they must be part of a (x^2 + a^2) expression, and plugging a = 2i into that gives (x^2 + 4). Now just divide the original polynomial by (x^2+4) and factor what is left.

Answer 2

7 is a zero