Answer
The fourth zero has to be a real (non-complex) number otherwise the function will have $5$ complex zeros.
Work Step by Step
The Conjugate Pairs Theorem says that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. That is, if $a + bi$ is a zero then so is $a – bi$ and vice-versa.
We have that $2$ and $1\pm 2i$ are zeros of $f(x)$, hence $f(x)$ has at least 3 zeros, so in order for it to have 4 zeros, the fourth zero has to be a real (non-complex number), because if it was a complex number its conjugate pair would also be a zero, making the degree at least 5 according to the Conjugate Pair Theorem.
