What do the number of zeros tell us about the degree of a polynomial

The video tutorial explains the concept of zeros in even and odd degree polynomials. It begins by discussing the characteristics of even degree polynomials, which can have an even number of zeros or none at all. Examples are provided to illustrate these concepts. The tutorial then shifts focus to odd degree polynomials, which always have an odd number of zeros, ensuring at least one solution. The video emphasizes understanding the relationship between the degree of a polynomial and the possible number of zeros it can have.

What is the significance of the degree of a polynomial when determining the number of roots?

How many roots can an even degree polynomial have?

How does the concept of X intercepts relate to the roots of a polynomial?

Explain why a polynomial of degree four can have either four, two, or zero roots.

What can you conclude about the roots of an odd degree polynomial?

What does it mean for a polynomial to have an odd number of roots?

Describe the relationship between the leading term of a polynomial and the number of possible roots.