Equation Root Finder using Bisection Method

equation-root-finder.cpp

//
// Created by Suren Khorenyan on 02.06.2023.
//

#include <iostream>
#include <cmath>

double equation(double a, double b, double x) {
    return a * pow(x, 3) + b * x - 1;
}

double findRoot(double a, double b, double left, double right, double epsilon) {
    double middle, middleValue;
    while (std::abs(right - left) > epsilon) {
        middle = (left + right) / 2.0;
        middleValue = equation(a, b, middle);

        if (middleValue == 0.0)
            return middle;

        if (equation(a, b, left) * middleValue < 0.0)
            right = middle;
        else
            left = middle;
    }
    return middle;
}

int main() {
    double a, b, epsilon;
    std::cout << "Enter the value for a: ";
    std::cin >> a;
    std::cout << "Enter the value for b: ";
    std::cin >> b;
    std::cout << "Enter the value for epsilon (tolerance): ";
    std::cin >> epsilon;

    double left, right;
    std::cout << "Enter the left boundary: ";
    std::cin >> left;
    std::cout << "Enter the right boundary: ";
    std::cin >> right;

    double root = findRoot(a, b, left, right, epsilon);

    std::cout << "The root of the equation " << a << "x^3 + " << b << "x - 1 = 0 ";
    std::cout << "in the interval [" << left << ", " << right << "] is: " << root << std::endl;

    return 0;
}

Run example:

Enter the value for a: 2
Enter the value for b: 3
Enter the value for epsilon (tolerance): 0.0001
Enter the left boundary: 0
Enter the right boundary: 1
The root of the equation 2x^3 + 3x - 1 = 0 in the interval [0, 1] is: 0.312927

Process finished with exit code 0