# What is the Bisection method and how do you use it?I am taking a test on this next week and I need verification on what the Bisection method is.

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### 1 Answer

The **Bisection Method** is a numerical method for estimating the roots of a polynomial **f(x).** It is one of the simplest and most reliable but it is not the fastest method. Assume that **f(x)** is continuous.

**Algorithm for the Bisection Method**: Given a continuous function **f(x)**

- Find points
**a**and**b**such that**a < b**and**f(a) * f(b) < 0**. - Take the interval
**[a, b]**and find its midpoint**x1**. - If
**f(x1) = 0**then**x1**is an exact root, else if**f(x1) * f(b) < 0**then let**a = x1,**else if**f(a) * f(x1) < 0**then let**b = x1**. - Repeat steps 2 & 3 until
**f(xi) = 0**or**|f(xi)| <= DOA,**where**DOA**stands for**degree of accuracy**.

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