Example: Find Roots of Quadratic Equation in C

// Find Roots of Quadratic Equation
#include <stdio.h>
#include <math.h> // Required for sqrt() function

int main() {
    // Step 1: Declare variables for coefficients and roots
    double a, b, c;
    double discriminant, root1, root2, realPart, imagPart;

    // Step 2: Prompt user for coefficients
    printf("Enter coefficient a: ");
    scanf("%lf", &a);
    printf("Enter coefficient b: ");
    scanf("%lf", &b);
    printf("Enter coefficient c: ");
    scanf("%lf", &c);

    // Step 3: Check if 'a' is zero
    if (a == 0) {
        printf("Error: Coefficient 'a' cannot be zero for a quadratic equation.\n");
        printf("This is a linear equation: %.2lfX + %.2lf = 0\n", b, c);
        // For a linear equation, if b is also 0, it's either no solution or infinite solutions.
        // Otherwise, x = -c/b
        if (b != 0) {
            printf("Root for linear equation: X = %.2lf\n", -c/b);
        } else {
            if (c == 0) {
                printf("Infinite solutions (0 = 0).\n");
            } else {
                printf("No solution (e.g., 5 = 0).\n");
            }
        }
        return 1; // Exit with an error code
    }

    // Step 4: Calculate the discriminant
    discriminant = b * b - 4 * a * c;

    // Step 5: Determine roots based on the discriminant's value
    if (discriminant > 0) {
        root1 = (-b + sqrt(discriminant)) / (2 * a);
        root2 = (-b - sqrt(discriminant)) / (2 * a);
        printf("Two distinct real roots: X1 = %.2lf and X2 = %.2lf\n", root1, root2);
    } else if (discriminant == 0) {
        root1 = root2 = -b / (2 * a); // Both roots are equal
        printf("One real root (or two equal real roots): X = %.2lf\n", root1);
    } else { // discriminant < 0
        realPart = -b / (2 * a);
        imagPart = sqrt(-discriminant) / (2 * a); // Use -discriminant because discriminant is negative
        printf("Two complex conjugate roots: X1 = %.2lf+%.2lfi and X2 = %.2lf-%.2lfi\n", realPart, imagPart, realPart, imagPart);
    }

    return 0; // Indicate successful execution
}