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