How to write a C program to find the roots of a quadratic equation?

A quadratic equation is of the form ax² + bx + c = 0, where a, b, and c are coefficients and a ? 0. The roots can be found using the quadratic formula, and the nature of roots depends on the discriminant value.

Syntax

r1 = (-b + sqrt(discriminant)) / (2 * a);
r2 = (-b - sqrt(discriminant)) / (2 * a);

Mathematical Formula

The quadratic formula is −

r? = (-b + ?(b² - 4ac)) / (2a)

r? = (-b - ?(b² - 4ac)) / (2a)

Where the discriminant (d) = b² - 4ac determines the nature of roots −

• If d > 0: Two distinct real roots
• If d = 0: Two equal real roots
• If d

Algorithm

1. Read coefficients a, b, c from user
2. Calculate discriminant d = b² - 4ac
3. Check the value of discriminant
4. Apply quadratic formula based on discriminant value
5. Display the roots

Flowchart

Example

Here's a complete C program that finds the roots of a quadratic equation −

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

int main() {
    float a, b, c, discriminant, root1, root2;
    
    printf("Enter coefficients a, b and c: ");
    scanf("%f %f %f", &a, &b, &c);
    
    // Calculate discriminant
    discriminant = b * b - 4 * a * c;
    
    if (discriminant > 0) {
        // Two distinct real roots
        root1 = (-b + sqrt(discriminant)) / (2 * a);
        root2 = (-b - sqrt(discriminant)) / (2 * a);
        printf("Two distinct real roots: %.2f and %.2f<br>", root1, root2);
    }
    else if (discriminant == 0) {
        // Two equal real roots
        root1 = root2 = -b / (2 * a);
        printf("Two equal real roots: %.2f and %.2f<br>", root1, root2);
    }
    else {
        // Complex roots
        float realPart = -b / (2 * a);
        float imagPart = sqrt(-discriminant) / (2 * a);
        printf("Complex roots: %.2f + %.2fi and %.2f - %.2fi<br>", 
               realPart, imagPart, realPart, imagPart);
    }
    
    return 0;
}

Output

Case 1: Two distinct real roots
Enter coefficients a, b and c: 1 -5 6
Two distinct real roots: 3.00 and 2.00

Case 2: Two equal real roots
Enter coefficients a, b and c: 1 -2 1
Two equal real roots: 1.00 and 1.00

Case 3: Complex roots
Enter coefficients a, b and c: 1 2 5
Complex roots: -1.00 + 2.00i and -1.00 - 2.00i

Key Points

• Always include <math.h> header for the sqrt() function
• Check if coefficient a is non-zero to ensure it's a quadratic equation
• Use proper operator precedence with parentheses in the quadratic formula
• Handle all three cases based on discriminant value

Conclusion

This program demonstrates how to solve quadratic equations in C by calculating the discriminant and applying the quadratic formula. It handles all possible cases including real, equal, and complex roots effectively.