Question 964450
f(x) = (x^2 + 22) (x^2 + 1)

How did I fid this?

You know that if f has complex roots, it is the product of simpler functions. Now a polynomial of degree 4 usually has terms in x and x^3. This happens when you multiply four functions. So instead you want to look at the product of two functions in x^2. Let's call them x^2 + a and x^2 + b. You know ab= 22 and a+b=23, this gives you a=22 and b=1 
whose two complex roots are
+- i sqrt(22)
+- i