I suppose that f(x) is a polynomial with integer coefficients
Therefore if 2-i is a solution then 2+i is a solution
And if is a solution then is a solution
Expand and determine using the value of f(1)
There's probably something similar for Real roots, but I do not know any formal properties in this area.
When have you ever (and only) gotten solutions of these forms, with radicals or imaginaries (or both)? From the "plus-minus" part of the Quadratic Formula!
Working backwards here from the zeroes, you know that, if one zero is "(something) plus (a square root)", then another zero must be "(that same thing) minus (that same square root)". Using the same reasoning with the complex root, you obtain the fourth zero.
From these, and the fact that, if x = a is a root, then x - a is a factor, you can find all four factors, and multiply them out to find the original polynomial.