To solve the quadratic equation ax² + bx + c = 0 using the quadratic formula, also known as the "almighty formula". The quadratic formula is given by:

*   If `a == 0`:
    *   If `b == 0`:
        *   If `c == 0`:
            *   Output "Infinite solutions (0 = 0)".
        *   Else (`c != 0`):
            *   Output "No solution (e.g., 5 = 0, which is false)".
    *   Else (`b != 0`):
        *   Calculate `root = -c / b`.
        *   Output "This is a linear equation. Root = ", `root`.
*   Else (`a != 0`, it's a quadratic equation):
    *   Calculate `discriminant = b*b - 4*a*c`.
    *   If `discriminant > 0`:
        *   Calculate `root1 = (-b + SQRT(discriminant)) / (2*a)`.
        *   Calculate `root2 = (-b - SQRT(discriminant)) / (2*a)`.
        *   Output "Two distinct real roots: ", `root1`, " and ", `root2`.
    *   Else If `discriminant == 0`:
        *   Calculate `root1 = -b / (2*a)`.
        *   Output "One real root (repeated): ", `root1`.
    *   Else (`discriminant < 0`):
        *   Calculate `realPart = -b / (2*a)`.
        *   Calculate `imaginaryPart = SQRT(ABS(discriminant)) / (2*a)`.
        *   Output "Two complex conjugate roots: ", `realPart`, " + ", `imaginaryPart`, "i", " and ", `realPart`, " - ", `imaginaryPart`, "i`.

#include <iostream> // Required for input/output operations (cin, cout)
#include <cmath>    // Required for mathematical functions like sqrt() and abs()

int main() {
    // Declare variables to store the coefficients
    double a, b, c;

    // Prompt the user to enter the coefficients
    std::cout << "Enter coefficient a: ";
    std::cin >> a;
    std::cout << "Enter coefficient b: ";
    std::cin >> b;
    std::cout << "Enter coefficient c: ";
    std::cin >> c;

    // Check if 'a' is zero to handle linear or trivial equations
    if (a == 0) {
        if (b == 0) {
            if (c == 0) {
                // Case: 0x^2 + 0x + 0 = 0 => 0 = 0 (Infinite solutions)
                std::cout << "Infinite solutions (0 = 0)." << std::endl;
            } else {
                // Case: 0x^2 + 0x + c = 0 (where c != 0) => c = 0 (No solution)
                std::cout << "No solution (e.g., " << c << " = 0, which is false)." << std::endl;
            }
        } else {
            // Case: 0x^2 + bx + c = 0 (where b != 0) => bx + c = 0 (Linear equation)
            double root = -c / b;
            std::cout << "This is a linear equation: " << b << "x + " << c << " = 0." << std::endl;
            std::cout << "Root = " << root << std::endl;
        }
    } else {
        // If 'a' is not zero, it's a quadratic equation.
        // Calculate the discriminant
        double discriminant = b * b - 4 * a * c;

        // Determine the nature of the roots based on the discriminant
        if (discriminant > 0) {
            // Two distinct real roots
            double root1 = (-b + sqrt(discriminant)) / (2 * a);
            double root2 = (-b - sqrt(discriminant)) / (2 * a);
            std::cout << "Roots are real and different." << std::endl;
            std::cout << "Root 1 = " << root1 << std::endl;
            std::cout << "Root 2 = " << root2 << std::endl;
        } else if (discriminant == 0) {
            // One real root (repeated)
            double root1 = -b / (2 * a);
            std::cout << "Roots are real and same." << std::endl;
            std::cout << "Root 1 = Root 2 = " << root1 << std::endl;
        } else {
            // Two complex conjugate roots
            double realPart = -b / (2 * a);
            double imaginaryPart = sqrt(std::abs(discriminant)) / (2 * a);
            std::cout << "Roots are complex and different." << std::endl;
            std::cout << "Root 1 = " << realPart << " + " << imaginaryPart << "i" << std::endl;
            std::cout << "Root 2 = " << realPart << " - " << imaginaryPart << "i" << std::endl;
        }
    }

    return 0; // Indicate successful program execution
}