Determine the number of positive and negative real zeros of a polynomial

The video tutorial explains how to determine real zeros of polynomials, distinguishing between real and imaginary zeros. It covers the process of identifying positive real zeros by analyzing sign changes in monomials and applying Cart's rule. The tutorial also demonstrates how to find negative real zeros by substituting negative values into the polynomial function and observing sign changes.

What are the two types of zeros discussed in the video?

• Rational and Irrational

• Real and Imaginary

• Whole and Fractional

• Positive and Negative

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

• By observing the alternation of signs in monomials

• By calculating the sum of coefficients

• By checking the degree of the polynomial

• By counting the number of terms

According to Descartes' Rule of Signs, what can the number of positive real zeros be?

• Always equal to the degree of the polynomial

• Equal to the number of sign changes or less by an even number

• Always zero

• Equal to the number of terms in the polynomial

What is the first step in determining the number of negative real zeros?

• Finding the derivative of the polynomial

• Counting the number of terms

• Substituting negative values into the polynomial

• Calculating the polynomial's degree

Why can't you have a negative number of real zeros?

• Because zeros are always positive

• Because negative zeros do not exist

• Because subtracting an even number from one sign change results in a negative count

• Because the polynomial's degree is always positive