Question

What are the possible number of positive real, negative real, and complex zeros of
f(x) = -7x^4 - 12x^3 + 9x^2 - 17x + 3?

Answer 1

Since the highest power of x in this polynomial is 4, you'll have four roots, total.

I believe there's a Theorem that predicts how many real roots you'll have, based upon the number of sign changes in the polynomial, but have forgotten the Theorem. Do you know of it?

Of course, if all else were to fail, you could find the actual roots and then classify them as positive or negative real or complex roots.