# C program for Newton Raphson method with output

In this program, you will implement the Newton-Raphson method for finding the root of the nonlinear equations in the C Programming language. The Newton-Raphson method is also known as Newton Method. you can find the root of the equation by taking the initial guess value.

## Program to find Newton-Raphson method by using for loop

``````
#include <stdio.h>
#include <math.h>
#include<stdlib.h>

//equation f(x)
float f(float x) {
// change the equation for solving another problem
return pow(x, 2) - 6;
}

//derivative of equation i.e f'(x)
float derivative(float x) {
// write the derivative of your equation
return 2 * x;
}

int main() {
float x;
int n, i;

printf("Enter initial guess value: ");
scanf("%f", &x);

printf("Enter number of iterations: ");
scanf("%d", &n);
for (i = 1; i <= n; i++)
{
if (derivative(x) == 0) {
// f'(x) should not be 0
printf("Division by Zero is not allowed.");
exit(0);
}

//Newton Raphson formula
x = x - f(x) / derivative(x);

// fabs() method will return positive value
printf("\nIteration %d and value %f", i, fabs(x));
}

printf("\n approximate root: %f \n", fabs(x));
return 0;
}
``````

## output

```Enter initial guess value: 1
Enter number of iterations: 5

Iteration 1 and value 3.500000
Iteration 2 and value 2.607143
Iteration 3 and value 2.454256
Iteration 4 and value 2.449494
Iteration 5 and value 2.449490
approximate root: 2.449490```

## Working of Newton-Raphson method:

• Take initial guess and number of iterations from user and store in variables `x` and `n`
• Iterate for loop from 1 to n. inside for loop check `derivative(x)` is zero or not. if 0 then the Newton-Raphson method will get failed.
• ` x = x - f(x) / derivative(x)` this is a formula of the Newton-Raphson method, it will calculate the root of an equation. For example, let's find the root of  x -6=0. if your initial guess will be 1 then f(x)=-2 and derivative(x)=2.
• Substitute the above value in Newton-Raphson formula i.e x=1- (-2)/2. value of x becomes 2. now pass new value i.e 2 in `f(2)` and `derivative(2)`, the function will return value and you will again substitute value in the newton formula. you will do this up to `n` time.
• After for loop end, you will get your approximate root value.
Point to remember:

If your guess value is closer to the root the Newton-Raphson method will take less time otherwise it will calculate but take more time.