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 given in the example?

• f(x) = x^2 - 8x + 2

• f(x) = x^3 - 8x^2 + 2x - 4

• f(x) = x^3 + 8x^2 - 2x + 4

• f(x) = x^3 - 8x^2 - 2x + 4

According to Descartes' Rule of Signs, how many sign changes are there in the polynomial f(x) = x^3 - 8x^2 + 2x - 4?

• 4

• 3

• 2

• 1

What are the possible numbers of positive real zeros for the polynomial?

• 3 or 2

• 3 or 1

• 2 or 0

• 1 or 0

What is the result of analyzing f(-x) for negative real zeros?

• There is 1 negative zero

• There are 0 negative zeros

• There are 3 negative zeros

• There are 2 negative zeros

What is the degree of the polynomial f(x) = x^3 - 8x^2 + 2x - 4?

• 1

• 2

• 3

• 4

If one zero is positive, what must the other two zeros be?

• One must be positive and one must be negative

• Both must be complex

• Both must be negative

• Both must be positive

How many total zeros can the polynomial have?

• 4

• 3

• 2

• 1