Use Descartes Rule of signs to determine the number of positive and negative

The video tutorial explains how to determine the number of positive and negative real zeros of a polynomial using Descartes' Rule of Signs. It involves analyzing the sign changes in the polynomial's terms to find possible positive zeros and applying the rule to a transformed polynomial to find possible negative zeros. The tutorial concludes with a summary of the findings.

What is the first step in using Descartes' Rule of Signs to find the number of positive real zeros?

• Calculate the derivative of the polynomial.

• Bring down the signs of each term in the polynomial.

• Identify the degree of the polynomial.

• Count the number of terms in the polynomial.

How do you determine the possible number of positive real zeros after counting the sign changes?

• Add an even number to the number of sign changes.

• Subtract an even number from the number of sign changes.

• Multiply the number of sign changes by 2.

• Divide the number of sign changes by 2.

When applying Descartes' Rule of Signs to find negative real zeros, what substitution is made in the polynomial?

• Replace x with 1/x.

• Replace x with -x.

• Replace x with x^2.

• Replace x with 0.

What indicates the absence of negative real zeros in a polynomial?

• The polynomial is a constant.

• All terms have positive coefficients.

• There are no sign changes after substituting -x.

• The polynomial has an even degree.

What is the main conclusion about the polynomial zeros in the final section?

• There are negative real zeros but no positive real zeros.

• There are both positive and negative real zeros.

• There are no real zeros at all.

• There are positive real zeros but no negative real zeros.