The bisection method is used to find the roots of a polynomial equation. It separates the interval and subdivides the interval in which the root of the equation lies. The principle behind this method is the intermediate theorem for continuous functions.
Let’s consider the continuous function f in the closed interval [a,b] is given with and of different signs. Then by the intermediate theorem, a point c exists for which f(c)=0.
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Steps to find the root:
Find two points a and b such that f(a) x f(b)<0
Find the midpoint of a and b, say c
If f(a) x f(c)<0, there exists a root between a and c. else if f(b) x f(c)<0 there exists a root between b and c.
Repeat above three steps until f(c)=0
Let’s Visualize the Bisection Method in the animation below,
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Visual representation of finding root using bisection method
