# Worksheet: Descartes’ Rule of Signs

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

**Q1: **

Using Descartesβs 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 Descartesβs 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 Descartesβs 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

**Q7: **

Is a factor of given that ?

- Ayes
- Bno

**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