Question

If 2i is a zero of f(x)=x^4+x^2+a, find the value of a. Then find the other 3 solutions.

Answer 1

i^4 = 1

i^2 = -1

If 2i is a zero:

$(2i)^4+(2i)^2+a=0$$2^4\times i^4+2^2\times i^2+a=0$$16\text{ - 4 = a}$$a=12$

So the equation is going to be:

$f(x)=x^4+x^2+12$