Roots of a Quadratic Equation Using an else-if Ladder in C

Algorithm

1. Read a, b and c. If a is zero, print that the equation is not quadratic.
2. Compute d = b² - 4ac.
3. If d > 0, print two real distinct roots; else if d == 0, print the equal root; else print the imaginary roots.

C program

#include <stdio.h>
#include <math.h>

int main(void) {
    double a, b, c, d, root1, root2, real, imag;

    printf("Enter a, b and c:\n");
    if (scanf("%lf %lf %lf", &a, &b, &c) != 3) {
        printf("Error: invalid input\n");
        return 1;
    }

    if (a == 0) {
        printf("Not a quadratic equation\n");
    } else {
        d = b * b - 4 * a * c;
        if (d > 0) {
            root1 = (-b + sqrt(d)) / (2 * a);
            root2 = (-b - sqrt(d)) / (2 * a);
            printf("Roots are real and distinct: %.2f %.2f\n", root1, root2);
        } else if (d == 0) {
            root1 = -b / (2 * a);
            printf("Roots are real and equal: %.2f\n", root1);
        } else {
            real = -b / (2 * a);
            imag = sqrt(-d) / (2 * a);
            if (imag < 0) {
                imag = -imag;
            }
            printf("Roots are imaginary: %.2f + i%.2f and %.2f - i%.2f\n", real, imag, real, imag);
        }
    }
    return 0;
}

Sample input and output

1 -3 2

Enter a, b and c:
Roots are real and distinct: 2.00 1.00

0 2 4

Enter a, b and c:
Not a quadratic equation

How the program works

The else-if ladder checks the discriminant from the most specific test to the general one. Exactly one branch runs, so the program never prints two answers for one equation.

Each branch computes only what it needs: the square root is taken only when d is non-negative in the real branches, and only -d inside the imaginary branch.

Viva questions

Common mistakes

• Writing three separate if statements, which can print more than one answer.
• Forgetting -lm when linking on systems where sqrt is in the maths library.