How to use and apply Descartes Rule of signs

The video tutorial explains how to determine the number of real and complex zeros of a polynomial function using Descartes' Rule of Signs. It covers the process of identifying sign changes in the function and its negative counterpart to find possible positive and negative real zeros. The tutorial also discusses how to calculate the number of complex solutions by considering the total degree of the polynomial. Examples are provided to illustrate the application of these concepts.

What is the first step in finding the number of positive real zeros of a function?

• Rewrite the function in terms of F(-X)

• Find the derivative of the function

• Set the function equal to zero

• Count the number of sign changes in F(X)

When analyzing F(-X), what is the result of raising a negative number to an odd power?

• It becomes undefined

• It becomes zero

• It remains negative

• It becomes positive

According to Descartes' Rule of Signs, what should you do after counting the sign changes?

• Subtract an odd number

• Add an even number

• Subtract an even number

• Multiply by two

How many real negative solutions can there be if there are two sign changes in F(-X)?

• Four or two

• One or zero

• Two or zero

• Three or one

What is the total number of solutions equal to in a polynomial function?

• The number of complex solutions

• The degree of the polynomial

• The number of negative solutions

• The number of positive solutions

If a polynomial has one positive and two negative real zeros, how many complex zeros does it have?

• One

• Two

• Zero

• Three

What is the purpose of creating a box to determine the number of solutions?

• To graph the function

• To solve the polynomial equation

• To find the derivative of the function

• To organize the possible number of positive, negative, and complex solutions