Algebra-2

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

First, we'll look for positive roots by analyzing P(x).

Coefficients for P(x):

6, -3, 4.

Counting Sign Changes:

From 6 to -3: 1 sign change (positive to negative).

From -3 to 4: 1 sign change (negative to positive).

Total Sign Changes for Positive Roots

There are 2 sign changes in total.

Possible Number of Positive Roots

According to Descartes' Rule of Signs, the number of positive roots can be:

2 or 0 positive roots.

Step 2: Analyzing Negative Roots

Next, we'll look for negative roots by analyzing P(-x).

Calculate P(-x):

Click "Show Answer" to reveal the answer and analysis