How to Find the Zeros of a Polynomial Function
Example 1
Determine between which consecutive integers the real zeros of f(x) = x3 + 3x2 - 4x + 6 are located.
There are three complex zeros for this function. According to Descartes’ Rule of Signs, there are two or
zero positive real roots and one negative real root. You can use substitution, synthetic division, or the
TABLE feature on a graphing calculator to evaluate the function for consecutive integral values of x.
Method 1: Synthetic Division
r
1
3
-4
6
-6
1
-3
14
-78
-5
1
-2
6
-24
-4
1
-1
0
6
-3
1
0
-4
18
-2
1
1
-6
18
-1
1
2
-6
12
0
1
3
-4
6
1
1
4
0
6
2
1
5
6
18
3
1
6
14
48
Method 2: Graphing Calculator
Use the TABLE feature.
The change in sign between -5 and -4 indicates that a zero exists between -5 and -4. This result is
consistent with Descartes’ Rule of Signs.
