Find all the possible real positive, real negative and complex zeros of a polynomial

The video tutorial explains the concept of complex solutions in polynomials, highlighting that complex solutions do not cross the x-axis. It introduces Descartes' Rule of Signs to determine the number of positive and negative real solutions by counting sign changes in the polynomial. The tutorial also covers how to find negative solutions using f(-x) and discusses the role of the polynomial's degree in determining the total number of zeros, including complex ones. The video concludes with a summary of these concepts and their application.

What type of solutions do not cross the x-axis?

• Real positive solutions

• Real negative solutions

• Complex solutions

• All solutions

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

• Subtract the degree of the polynomial

• Count the number of terms in the polynomial

• Count the number of sign changes between terms

• Evaluate the polynomial at x = 0

What is the first step in finding the number of negative real solutions using Descartes' Rule of Signs?

• Subtract the degree of the polynomial

• Evaluate the polynomial at negative x

• Evaluate the polynomial at x = 0

• Count the number of terms

When evaluating a polynomial at negative x, what happens to a negative number raised to an even power?

• It becomes undefined

• It remains negative

• It becomes positive

• It becomes zero

How do complex solutions typically appear in polynomials?

• As imaginary numbers only

• As real numbers

• As conjugate pairs

• As single numbers

If a polynomial has a degree of 3, how many total zeros should it have?

• 1

• 2

• 3

• 4

What does Descartes' Rule of Signs help determine about a polynomial?

• The exact values of the zeros

• The possible number of positive, negative, and complex zeros

• The degree of the polynomial

• The coefficients of the polynomial