Use a graphing calculator to approximate real solution of the equation. (See Example 1.)6x...

Use a graphing calculator to approximate real solution of the equation. (See Example 1.)

6x3 − 5x2 + 3x − 2 = 0

Example 1

Use a graphical root finder to solve x3 − 5x + 1 = 0.

Solution

First, graph y = x3 − 5x + 1. The x-intercepts of this graph are the solutions of the equation. To find these intercepts, look for “root” or “zero” in the appropriate menu.* Check your instruction manual for the proper syntax. A typical root finder (see Figure 1) shows that two of the solutions (x-intercepts) are x ≈ .2016 and x ≈ 2.1284. For the third solution, see the problem at the side.

FIGURE 1

*CALC or TI-84+, GRAPH MATH on TI-86, G-SOLV on Casio.