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

+2i is also a solution
dividing 4 into 196 gives 49
so it looks like 7 and -7 may be roots

plugging these values gives

7^4 - 45*49 - 196 = 0

Answer 2

roots are 7,-7,-2i, 2i

Answer 3

i ought to explain some more about the above;

complex roots exist as pairs
if a + bi is a root then the other is a - bi
thats why +2i is another root of your equation

to find the other roots i used the rational root theorem
the factors of 196 are +/-1, +/- 2, +/-4, +/-7, +/-14, +/-28, +/- 49 and are possible roots

i was lucky that i guessed it might be +7 and -7 first

an equation in x^4 will have 4 roots , if some are complex there will be 2 of them