Example 1.  Find all the real solutions to the cubic equation  .  

Solution 1.

Plot the function.

There appears to be only one real root which lies in the interval [1,2].

Call the Regula Falsi subroutine on the interval [1,2] using 10 iterations

k

After 10 iterations, the interval has been reduced to [a,b] where

The root lies somewhere in the interval [a,b] width of which is

The reported root is alleged to be

The estimate of "how things are going" is the distance between  c  and the nearest endpoint to the interval.

Is this the desired accuracy you want ?  If not, more iterations are required.

k

Compare our result with Mathematica's built in root finder.

(c) John H. Mathews 2004