Program to Find Roots of a Quadratic Equation in C++

Finding Roots of a Quadratic Equation

A quadratic equation is in the form ax² + bx + c = 0. The roots of this equation can be real or complex depending on the discriminant (D = b² - 4ac).

We will explore three different methods to find the roots of a quadratic equation in C++.

Method 1: Using the Quadratic Formula

This method uses the quadratic formula: x = (-b ± sqrt(b² - 4ac)) / (2a).

#include <iostream>
#include <cmath>

using namespace std;

void findRoots(int a, int b, int c) {
    float discriminant = b * b - 4 * a * c;
    if (discriminant > 0) {
        float root1 = (-b + sqrt(discriminant)) / (2 * a);
        float root2 = (-b - sqrt(discriminant)) / (2 * a);
        cout << "Real and Distinct Roots: " << root1 << ", " << root2 << endl;
    } else if (discriminant == 0) {
        float root = -b / (2.0 * a);
        cout << "Real and Equal Roots: " << root << endl;
    } else {
        float realPart = -b / (2.0 * a);
        float imagPart = sqrt(-discriminant) / (2.0 * a);
        cout << "Complex Roots: " << realPart << " + " << imagPart << "i, "
             << realPart << " - " << imagPart << "i" << endl;
    }
}

int main() {
    int a, b, c;
    cout << "Enter coefficients a, b, and c: ";
    cin >> a >> b >> c;
    findRoots(a, b, c);
    return 0;
}
            

Method 2: Using Factorization

Factorization is an alternative method where we break the middle term to find the roots.

#include <iostream>
using namespace std;

void findRootsByFactorization(int a, int b, int c) {
    bool found = false;
    for (int i = -100; i <= 100; i++) {
        for (int j = -100; j <= 100; j++) {
            if (i * j == a * c && i + j == b) {
                cout << "Roots are: " << -j << "/" << a << " and " << -i << "/" << a << endl;
                found = true;
                break;
            }
        }
        if (found) break;
    }
    if (!found) cout << "Cannot be factorized easily." << endl;
}

int main() {
    int a, b, c;
    cout << "Enter coefficients a, b, and c: ";
    cin >> a >> b >> c;
    findRootsByFactorization(a, b, c);
    return 0;
}
            

Method 3: Using Recursion

This method recursively calculates the discriminant and finds the roots.

#include <iostream>
#include <cmath>

using namespace std;

void findRootsRecursive(int a, int b, int c, float d) {
    if (d > 0) {
        float root1 = (-b + sqrt(d)) / (2 * a);
        float root2 = (-b - sqrt(d)) / (2 * a);
        cout << "Real and Distinct Roots: " << root1 << ", " << root2 << endl;
    } else if (d == 0) {
        float root = -b / (2.0 * a);
        cout << "Real and Equal Roots: " << root << endl;
    } else {
        float realPart = -b / (2.0 * a);
        float imagPart = sqrt(-d) / (2.0 * a);
        cout << "Complex Roots: " << realPart << " + " << imagPart << "i, "
             << realPart << " - " << imagPart << "i" << endl;
    }
}

void calculateDiscriminant(int a, int b, int c) {
    float d = b * b - 4 * a * c;
    findRootsRecursive(a, b, c, d);
}

int main() {
    int a, b, c;
    cout << "Enter coefficients a, b, and c: ";
    cin >> a >> b >> c;
    calculateDiscriminant(a, b, c);
    return 0;
}