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

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

Q3:

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

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