Using Descartes Rule of Signs to determine possible number of solutions

The video tutorial explains the rational zero test and Descartes' rule of signs, focusing on determining possible real and complex zeros in polynomials. It covers quadratic solutions, including real and complex possibilities, and extends to higher degree polynomials. The tutorial demonstrates using F(-X) to find negative real zeros and employs a table to organize possible solutions, emphasizing understanding over exact answers.

What is the rational zero test and what does it tell us?

Explain Descartes' rule of signs and its significance in determining the number of real zeros.

How do you determine the number of positive real zeros in a polynomial?

What is the process for finding the number of negative real zeros?

Discuss the relationship between the degree of a polynomial and the number of real and complex solutions.

How can you use a table to find the number of complex zeros in a polynomial?

What conclusions can you draw about the number of complex solutions based on the number of positive and negative zeros?