Example: Solve Quadratic Equation using Function in C++

// Solve Quadratic Equation using Function
#include <iostream> // For input/output operations
#include <cmath>    // For sqrt() and fabs() functions
#include <iomanip>  // For std::fixed and std::setprecision

using namespace std;

// Function to solve quadratic equation
// Takes coefficients a, b, c and outputs roots via reference parameters
void solveQuadratic(double a, double b, double c, double& root1, double& root2) {
    // Step 1: Calculate the discriminant (delta)
    double discriminant = b * b - 4 * a * c;

    // Step 2: Determine the nature of roots based on the discriminant
    if (discriminant >= 0) {
        // Real roots (distinct or equal)
        root1 = (-b + sqrt(discriminant)) / (2 * a);
        root2 = (-b - sqrt(discriminant)) / (2 * a);
    } else {
        // Complex roots
        double realPart = -b / (2 * a);
        double imaginaryPart = sqrt(fabs(discriminant)) / (2 * a);
        // For complex roots, we'll store the real part in root1 and
        // the imaginary part (positive value) in root2 to display them in main.
        // This is a common way to handle complex numbers when not using a complex type.
        root1 = realPart;
        root2 = imaginaryPart; // root2 now stores the magnitude of the imaginary part
    }
}

int main() {
    // Step 1: Declare variables for coefficients and roots
    double a, b, c;
    double root1, root2; // These will hold the calculated roots

    // Step 2: Get user input for coefficients
    cout << "Enter coefficient a: ";
    cin >> a;
    cout << "Enter coefficient b: ";
    cin >> b;
    cout << "Enter coefficient c: ";
    cin >> c;

    // Step 3: Handle the special case where 'a' is zero
    if (a == 0) {
        cout << "Error: 'a' cannot be zero for a quadratic equation." << endl;
        // If a is 0, it becomes a linear equation: bx + c = 0 => x = -c/b
        if (b != 0) {
            cout << "This is a linear equation. Root x = " << fixed << setprecision(2) << -c / b << endl;
        } else {
            cout << "No solution or infinite solutions." << endl;
        }
        return 1; // Indicate an error
    }

    // Step 4: Call the function to solve the quadratic equation
    solveQuadratic(a, b, c, root1, root2);

    // Step 5: Display the results based on the discriminant's original sign
    double discriminant = b * b - 4 * a * c;
    cout << fixed << setprecision(2); // Format output to 2 decimal places

    if (discriminant >= 0) {
        if (discriminant == 0) {
            cout << "The quadratic equation has one real (repeated) root." << endl;
            cout << "Root = " << root1 << endl; // root1 and root2 would be equal
        } else {
            cout << "The quadratic equation has two distinct real roots." << endl;
            cout << "Root 1 = " << root1 << endl;
            cout << "Root 2 = " << root2 << endl;
        }
    } else {
        cout << "The quadratic equation has two distinct complex roots." << endl;
        cout << "Root 1 = " << root1 << " + " << root2 << "i" << endl;
        cout << "Root 2 = " << root1 << " - " << root2 << "i" << endl;
    }

    return 0;
}