Write a C/C++ program that approximates a root of the equation f(x) =

Question

Write a C/C++ program that approximates a root of the equation f(x) = 0 in an interval [a, b] using Newton-Raphson method. The necessary assumptions for application of this method should be explicitly mentioned. Use the method to find one root of the equation: x3 + 4x2 - 19=0.

02 Aug 2023

Answer :

Word Count : 548

Here's a C++ program that uses the Newton-Raphson method to approximate a root of the equation f(x) = 0 within a given interval [a, b]. The program will find one root of the equation x^3 + 4x^2 - 19 = 0.

#include
#include
using namespace std;

const double EPSILON = 0.00001;
const int MAX_ITERATIONS = 100;

double f(double x) {
return pow(x, 3) + 4 * pow(x, 2) - 19;
}

double f_prime(double x) {
return 3 * pow(x, 2) + 8 * x;
}

double newtonRaphson(double a, double b) {
double x0 = (a + b) / 2; // Initial guess for the root

for (int i = 0; i < MAX_ITERATIONS; i++) {
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