Determine the number of positive, negative and complex roots of a polynomial

The video tutorial explains how to determine the possible number of positive, negative, and imaginary zeros of a polynomial using Descartes' Rule of Signs. The instructor demonstrates the process by analyzing sign changes in the polynomial and substituting negative values to find negative zeros. The tutorial concludes with a discussion on the total number of zeros, including complex roots, based on the polynomial's degree.

What is the polynomial function discussed in the text?

What is the significance of the number of sign changes in determining the number of positive real zeros?

How many positive real zeros can the polynomial have according to the Descartes' rule of signs?

What happens to the signs of the terms when substituting negative x into the polynomial?

What conclusion can be drawn about the number of negative real zeros for the polynomial?

How many total zeros can the polynomial have based on its degree?

If one zero is positive, what can be said about the other two zeros?