How do I solve: "For each equation, state the number of complex roots & the possible rational roots."

Question

I just don't really understand what the question is asking or how to find the answer.

Answer 1

I assume the question concerns polynomial equations with real coefficients.

Descartes' rule of signs will give you an upper limit of the # of positive and negative real roots.

If n/d is a rational root of the polynomial, then n must divide the constant term and d must divide the coefficient of the highest power term.

Unless the equation is of very high degree, these two rules should give you a pretty good fix on the number of real roots. The the remaining foots must be complex conjugates which must occur in pairs.