Using Descartes Rule of Signs to determine possible number of solutions

The video tutorial explains the rational zero test and Descartes' rule of signs, focusing on determining possible real and complex zeros in polynomials. It covers quadratic solutions, including real and complex possibilities, and extends to higher degree polynomials. The tutorial demonstrates using F(-X) to find negative real zeros and employs a table to organize possible solutions, emphasizing understanding over exact answers.

What does Descartes' rule of signs help determine in a polynomial?

• The degree of the polynomial

• The coefficients of the polynomial

• The possible number of real positive, real negative, and complex zeros

• The exact values of the zeros

How do you determine the number of real positive zeros using Descartes' rule of signs?

• Count the number of terms in the polynomial

• Count the number of negative coefficients

• Count the number of sign changes in the polynomial

• Count the number of positive coefficients

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

• Use the polynomial F(-X)

• Use the derivative of the polynomial

• Use the original polynomial F(X)

• Use the polynomial F(X) squared

What happens when a negative number is raised to an even power?

• It becomes undefined

• It becomes zero

• It becomes positive

• It remains negative

In a cubic polynomial, if there is one real solution, what must the other two solutions be?

• Imaginary

• Complex

• Undefined

• Real

How many total zero solutions should a polynomial of degree 3 have?

• One

• Four

• Two

• Three

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

• Zero

• One

• Three

• Two