# Lesson Worksheet: Descartes’ Rule of Signs Mathematics • 10th Grade

In this worksheet, we will practice using Descartes’ rule of signs to get all possible numbers of positive and negative real roots.

Q1:

Using Descartes’s rule of signs, find which of the following describes the possible real zeros of .

• A has either 3 or 1 positive zeros and 0 negative zeros.
• B has either 2 or 0 positive zeros and 1 negative zero.
• C has either 2 or 0 positive zeros and either 3 or 1 negative zeros.
• D has either 3 or 1 positive zeros and either 2 or 0 negative zeros.
• E has 0 positive zeros and either 3 or 1 negative zeros.

Q2:

Using Descartes’s rule of signs, find which of the following describes the possible real zeros of .

• A has 0 positive zeros and either 3 or 1 negative zeros.
• B has 1 positive zero and 0 negative zeros.
• C has either 3 or 1 positive zeros and 0 negative zeros.
• D has either 2 or 0 positive zeros and one negative zero.
• E has 1 positive zero and either 2 or 0 negative zeros.

Q3:

Using Descartes’s rule of signs, find which of the following describes the possible real zeros of .

• A has either 3 or 1 positive zeros and 1 negative zero.
• B has either 2 or 0 positive zeros and either 2 or 0 negative zeros.
• C has 0 positive zeros and either 2 or 0 negative zeros.
• D has 1 positive zero and either 3 or 1 negative zeros.
• E has either 2 or 0 positive zeros and 0 negative zeros.

Q4:

How many roots does the polynomial have?

Q5:

Which of the following lists contain all the roots of ?

• A
• B
• C
• D

Q6:

Find, by factoring, the zeros of the function .

• A
• B
• C
• D
• E

Q7:

Is a factor of given that ?

• AYes
• BNo

Q8:

Find, by factoring, the zeros of the function .

• A
• B
• C
• D
• E

Q9:

Which of the following are roots of ?

• A4, and
• B6, and
• C, and
• D, and
• E4, and 7

Q10:

Is a factor of given that ?

• AYes
• BNo

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