## Overview

The regula-falsi method is the oldest method of finding the approximate numerical value of a real root of an equation f(x) = 0.

This method is also known as method of false position. The method used to estimate the roots of a polynomial f(x).

In this method we suppose that x_{1} and x_{2} are two points where f(x_{1}) and f(x_{2}) are of opposite sign .Let f(x_{1}) < 0 and f(x_{2}) > 0.

Hence the root of the equation f(x) = 0 lies between x_{1} and x_{1} and so, f(x_{1})f(x_{2}) < 0.

## Formula of regula-falsi method

The Regula Falsi formula

Find f(x_{3}) is positive or negative. If f(x_{3}) > 0 then root lies between x_{3} and x_{1} or if f(x_{3}) < 0 then root lies between x_{3} and x_{1} similarly we calculate x_{4}.

Proceed in this manner until the desired accurate root is found.

## Solved example

** Example: Apply Regula Falsi Method to solve the equation**– 3x – cosx – 1 = 0.

Solution:

let f(x) = 3x – cosx – 1 = 0

by hit and trial

f(0.60) = 0.010351 > 0

So the root of the equation lies between x_{1}=0.60 and x_{2} = 0.61, also

f(0.60) f(0.61) < 0

By Regula Falsi Mehtod, the first approximation,

now

So, root of the equation f(x) = 0 lies between 0.60709 and 0.61 and also f(0.60709) f(0.61) < 0.

Second approximation

now

So, root of the equation f(x) = 0 lies between 0.60710 and 0.61 and also f(0.60710) f(0.61) < 0.

The third approximation,

Hence the root of the given equation correct to five decimal place is 0.60710.

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