# Worksheet: Descartes's Rule of Signs

In this worksheet, we will practice using Descartes’s 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 0 positive zeros and either 3 or 1 negative zeros.
- B has either 3 or 1 positive zeros and 0 negative zeros.
- C has either 2 or 0 positive zeros and 1 negative zero.
- D has either 2 or 0 positive zeros and either 3 or 1 negative zeros.
- E has either 3 or 1 positive zeros and either 2 or 0 negative zeros.

**Q2: **

Using Descartesβs rule of signs, find which of the following describes the possible real zeros of .

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

**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 1 positive zero and either 3 or 1 negative zeros.
- C has either 2 or 0 positive zeros and either 2 or 0 negative zeros.
- D has 0 positive zeros and either 2 or 0 negative zeros.
- E has either 2 or 0 positive zeros and 0 negative zeros.