How to use Descartes rule of signs to determine the number of positive and negative zeros

The video tutorial explains the limitations of rational root tests and introduces Descartes' Rule of Signs to determine the number of positive and negative real zeros in a polynomial. It details the process of identifying sign changes to find positive real zeros and evaluates F of negative X to find negative real zeros. The tutorial concludes with a final problem to reinforce the concepts.

What does Descartes' Rule of Signs help us determine?

• The number of complex roots

• The number of positive and negative real zeros

• The number of irrational roots

• The number of rational roots

How do you determine the number of positive real zeros using Descartes' Rule of Signs?

• Count the number of odd integers in the polynomial

• Count the number of sign changes in the polynomial

• Count the number of even integers in the polynomial

• Count the number of terms in the polynomial

What is the smallest even integer you can subtract when using Descartes' Rule of Signs?

• 0

• 1

• 2

• 3

When evaluating for negative real zeros, what is the first step?

• Evaluate the polynomial at positive x

• Subtract an odd integer from the polynomial

• Count the number of terms in the polynomial

• Evaluate the polynomial at negative x

What happens to a negative number raised to an odd power?

• It becomes positive

• It becomes imaginary

• It becomes zero

• It remains negative