# False Position Method Python Program (with Output)

#### This program implements false position (Regula Falsi) method for finding real root of nonlinear equation in python programming language.

In this python program, x0 and x1 are two initial guesses, e is tolerable error and nonlinear function f(x) is defined using python function definition `def f(x):`.

## Python Source Code: False Position (Regula Falsi) Method

``````
# Defining Function
def f(x):
return x**3-5*x-9

# Implementing False Position Method
def falsePosition(x0,x1,e):
step = 1
print('\n\n*** FALSE POSITION METHOD IMPLEMENTATION ***')
condition = True
while condition:
x2 = x0 - (x1-x0) * f(x0)/( f(x1) - f(x0) )
print('Iteration-%d, x2 = %0.6f and f(x2) = %0.6f' % (step, x2, f(x2)))

if f(x0) * f(x2) < 0:
x1 = x2
else:
x0 = x2

step = step + 1
condition = abs(f(x2)) > e

print('\nRequired root is: %0.8f' % x2)

# Input Section
x0 = input('First Guess: ')
x1 = input('Second Guess: ')
e = input('Tolerable Error: ')

# Converting input to float
x0 = float(x0)
x1 = float(x1)
e = float(e)

#Note: You can combine above two section like this
# x0 = float(input('First Guess: '))
# x1 = float(input('Second Guess: '))
# e = float(input('Tolerable Error: '))

# Checking Correctness of initial guess values and false positioning
if f(x0) * f(x1) > 0.0:
print('Given guess values do not bracket the root.')
print('Try Again with different guess values.')
else:
falsePosition(x0,x1,e)
``````

## False Position Program Output

```First Guess: 2
Second Guess: 3
Tolerable Error: 0.00001

*** FALSE POSITION METHOD IMPLEMENTATION ***
Iteration-1, x2 = 2.785714 and f(x2) = -1.310860
Iteration-2, x2 = 2.850875 and f(x2) = -0.083923
Iteration-3, x2 = 2.854933 and f(x2) = -0.005125
Iteration-4, x2 = 2.855180 and f(x2) = -0.000312
Iteration-5, x2 = 2.855196 and f(x2) = -0.000019
Iteration-6, x2 = 2.855196 and f(x2) = -0.000001

Required root is: 2.85519648
```