How could you use descartes' rule and the fundamental theorem of algebra to predict the number of complex roots to a polynomial, as well as find the number of possible positive and negative real roots to a polynomial?

so the number of positive real roots is either 4, or (4-2) 2, or (2-2) 0. And the negative real roots are only 1. Any slack gets picked up by the versatile complex twins.

4 real positive ones and 1 negative real one

or

2 real positive ones and 1 negative real one and 2 complex ones

or

0 real positive ones and 1 negative real one and 4 complex ones.