The decimal search

Authors Avatar

The Decimal Search method

I would like to solve the equation x³ + 2x² − 0.5 = 0. Let f(x) = x³ + 2x² − 0.5

        
The graph below shows the equation y = x³ + 2x² − 0.5. As you can see, there are three roots/solutions when f(x) = 0.

The equation x³ + 2x² − 0.5 = 0 cannot be solved algebraically so I will use the decimal search method.

        

This method looks for a change in sign of the value of f(x). The following table gives values of x and f(x).

Join now!

As the curve crosses the x axis, the value of the function f(x) changes sign, for example:

The values of f(x) in the table above confirms there are roots between [-2,-1.5] [-1,-0.5] and [0, 0.5].

I am going to concentrate on finding a more accurate value of the root between [-2,-1.5]. I will achieve this by reducing the size of the intervals to a width of 0.1. The graph and table below show that the root is between [-1.8,-1.9].

...

This is a preview of the whole essay