It's a method used to apptoximate roots of an equation by continually "narrowing" the interval on which a "root" occurs......here's an example.....
Let us suppose that we wanted to solve this equation....
x^2 - 5 = 0
And let us suppose that we know that one root lies between 2 and 3......divide this interval in half = 2.5 and substitue this value into the equation. So we have (2.25)^2 - 5 = 1.25.
Then, since this value is positive and the value "2" would produce a "negative," then we know that the "root occurs between 2 and 2.25. So, divide this interval in half = 2.125, and substitue this value into the equation . So we have (2.125)^2 - 5 = a negative vlaue. So, we know that the root must lie between 2.125 and 3.
And dividing this interval in half we have...2.5625....and substituting this value into the equation we have...(2.5625)^2 - 5 = a positive......so now we know that the root lies btween 2.125 and 2.5625. So, we divide this interval in half, etc.
Notice that width of the interval has decreased from 1 to .4375 in just three steps......by continuing this iterative puocess just a few more times, we would get close to the "real" root of about 2.236...
This method is based on the Intermediate Value Theorem.....which says that if we have a continuous interval [a,b] and f(a) and f(b) have opposite signs, then there must be some "c" on [a,b] such that f(c) = 0.......
