Goseeko blog # What is regula-falsi method?

## 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 x1 and x2 are two points where f(x1) and f(x2) are of opposite sign .Let f(x1) < 0 and f(x2) > 0.

Hence the root of the equation f(x) = 0 lies between x1 and x1 and so, f(x1)f(x2) < 0.

## Formula of regula-falsi method

The Regula Falsi formula

Find f(x3) is positive or negative. If f(x3) > 0 then root lies between x3 and x1 or if f(x3) < 0 then root lies between x3 and x1  similarly we calculate x4.

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 x1=0.60 and x2 = 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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