Use Descartes Rule of Signs to determine the possible number...

To determine the possible number of positive and negative roots for the polynomial , we will apply Descartes' Rule of Signs.

Step 1: Analyzing Positive Roots

1. Look at the coefficients of : , , , , .

2. Count sign changes:

From to , no sign change.

From to , sign change.

3. Total sign changes for positive roots is .

4. According to Descartes' Rule of Signs, the number of positive roots can be or .

Step 2: Analyzing Negative Roots

1. Calculate :

Algebra-2