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* i^4+2^2* i^2+a=0`
`16\text{ - 4 = a}`
`a=12`

So the equation is going to be:

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