Descartes' Rule of Signs Quiz

This video tutorial explains Descartes' Rule of Signs, which helps determine the number of positive, negative, and imaginary zeros in a polynomial function. The video provides examples using a cubic and a fifth-degree polynomial, demonstrating how to apply the rule and verify the results through factoring and synthetic division.

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

• The possible number of positive, negative, and imaginary zeros

• The number of terms in the polynomial

• The degree of the polynomial

• The coefficients of the polynomial

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CCSS.HSF-IF.C.7C

In the example with the cubic polynomial, how many sign changes are there for f(x)?

• One

• Three

• Four

• Two

According to Descartes' Rule of Signs, what are the possible numbers of positive real zeros for the cubic polynomial?

• One or zero

• Four or two

• Two or zero

• Three or one

How many negative real zeros are there for the cubic polynomial?

• One

• Three

• Zero

• Two

What is the total number of zeros for the cubic polynomial?

• Three

• Four

• One

• Two

For the fifth-degree polynomial, how many sign changes are there for f(x)?

• Four

• Two

• One

• Three

What are the possible numbers of positive real zeros for the fifth-degree polynomial?

• Four, two, or zero

• Two, one, or zero

• Five, three, or one

• Three, two, or one

How many negative real zeros are possible for the fifth-degree polynomial?

• Two

• One

• Three

• Zero

What is the total number of zeros for the fifth-degree polynomial?

• Six

• Five

• Four

• Three

Which row correctly applies to the fifth-degree polynomial based on the zeros found?

• 4 positive, 1 negative, 0 imaginary

• 2 positive, 1 negative, 2 imaginary

• 0 positive, 1 negative, 4 imaginary

• 3 positive, 2 negative, 0 imaginary