Locating zeros of polynomial function: determine the number of complex zeros

In a previous question about this function, you determined that there were two (2) real zeros, near -1.4 and +3.4. (q: question/11280846)

Since this is a 4th degree polynomial, there are 4 zeros total, so two complex zeros.

The factorization is

... f(x) = (x² -2x -5)(x² -x +1)

The latter factor has zeros at 0.5±i·0.5√3.