How to find the roots of equations using Geometry Sketchpad

Geometry Sketchpad is a powerful geometric calculation software that is very useful when solving the roots of polynomial equations. This article will introduce in detail how to use Geometry Sketchpad to find the roots of an equation, including how to create equations, draw, and use various tools to solve equations. If you're looking for an easy-to-understand method to solve the roots of a polynomial equation, this guide will provide you with the steps and techniques you need.

1. Taking the equation x3-3x 1=0 as an example, first construct the function f(x)= x3-3x 1 and draw its image. Click [Draw] - [Draw New Function]. Enter the function expression in the pop-up window and click OK. In this way, the function graph is drawn.

2. Select the root tool. Click [Customize Tools] and select the [Function Tool]-[Root of f(x)=0] option.

3. Click the function expression, and an active point will appear. Move the point until the root is displayed. At this time, the first root of the equation is displayed. Click the expression again. , move the point to find the second root, and the third root can be found in the same way.

4. Change and set the root subscript. Click each xroot value in turn, click [Display] - [Measurement Value Label], in the small window, change the starting value of subscript rod to 1, and click OK.

5. Hide redundant yroot initial value expressions. Select three initial values ​​and click [Show] - [Hide Measurement Values].

6. Set the accuracy of the root. Select each root, click [Display] - [Label of Measurement Value], click the value label, select one hundredth if you want to keep two decimal places, and OK.

7. Finally, the results are displayed as shown below.

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