Use descartes rule of signs to find the number of positive and negative real zeros

The video tutorial explains how to determine the number of positive and negative real zeros in a polynomial using Descartes' Rule of Signs. It covers the rational zero test and demonstrates how to apply Descartes' Rule by counting sign changes in the polynomial's standard form. The tutorial also explains how to handle negative inputs to find negative real zeros.

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

• The degree of the polynomial

• The exact values of the zeros

• The number of real zeros

• The number of positive and negative real zeros

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

• By counting the number of terms in the polynomial

• By calculating the derivative of the polynomial

• By counting the number of sign changes in the polynomial

• By finding the degree of the polynomial

If a polynomial has 4 sign changes, how many positive real zeros could it have?

• 6, 4, or 2

• 4, 2, or 0

• 3, 1, or 0

• 5, 3, or 1

What is the significance of subtracting factors of two in Descartes' Rule of Signs?

• It accounts for the polynomial's degree

• It reduces the number of possible real zeros

• It helps find the exact zeros

• It adjusts for complex zeros

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

• Count the sign changes in the original polynomial

• Substitute negative x into the polynomial

• Find the derivative of the polynomial

• Calculate the polynomial's degree

When substituting negative x into a polynomial, what happens to terms with even powers?

• They become negative

• They are eliminated

• They remain unchanged

• They become positive

How many negative real zeros can a polynomial have if there are 3 sign changes after substituting negative x?

• 3 or 1

• 2 or 0

• 5 or 3

• 4 or 2