How to use Descartes Rule of signs to find positive & negative zeros

The video tutorial explains how to determine the variations in the sign of polynomial coefficients to find possible real zeros. It covers the process of calculating real zeros by subtracting even integers from the number of sign variations. The tutorial also discusses testing for negative real zeros using F(-X) and highlights the use of synthetic division and the rational zero test to identify zeros without a graphing calculator.

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

• By calculating the degree of the polynomial

• By counting the number of terms in the polynomial

• By finding the variations in the sign of the coefficients

• By evaluating the polynomial at zero

What is the significance of subtracting an even integer from the number of sign variations?

• It identifies the leading coefficient

• It determines the degree of the polynomial

• It provides alternative possible numbers of positive real zeros

• It gives the number of complex zeros

What does it mean if there are no sign variations when testing F(-X)?

• The polynomial is constant

• There are no negative real zeros

• There are no positive real zeros

• All zeros are complex

Why is synthetic division useful when finding real zeros?

• It finds the derivative of the polynomial

• It determines the degree of the polynomial

• It helps identify possible real zeros without a graphing calculator

• It simplifies the polynomial

When using the rational zero test, why might you only test positive numbers?

• The test only applies to positive coefficients

• If no negative real zeros are found, all zeros must be positive

• Because negative numbers are not allowed in the test

• Positive numbers are easier to calculate