Program to Find Roots of a Quadratic Equation in C

Finding Roots of a Quadratic Equation

A quadratic equation is in the form ax² + bx + c = 0. The roots of this equation can be real or complex depending on the discriminant (D = b² - 4ac).

We will explore three different methods to find the roots of a quadratic equation in C.

Method 1: Using the Quadratic Formula

This method uses the quadratic formula: x = (-b ± sqrt(b² - 4ac)) / (2a).

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

void findRoots(int a, int b, int c) {
    float discriminant = b * b - 4 * a * c;
    if (discriminant > 0) {
        float root1 = (-b + sqrt(discriminant)) / (2 * a);
        float root2 = (-b - sqrt(discriminant)) / (2 * a);
        printf("Real and Distinct Roots: %.2f, %.2f\n", root1, root2);
    } else if (discriminant == 0) {
        float root = -b / (2 * a);
        printf("Real and Equal Roots: %.2f\n", root);
    } else {
        float realPart = -b / (2 * a);
        float imagPart = sqrt(-discriminant) / (2 * a);
        printf("Complex Roots: %.2f + %.2fi, %.2f - %.2fi\n", realPart, imagPart, realPart, imagPart);
    }
}

int main() {
    int a, b, c;
    printf("Enter coefficients a, b, and c: ");
    scanf("%d %d %d", &a, &b, &c);
    findRoots(a, b, c);
    return 0;
}
            

Method 2: Using Factorization

Factorization is an alternative method where we break the middle term to find the roots.

#include <stdio.h>

void findRootsByFactorization(int a, int b, int c) {
    int found = 0;
    for (int i = -100; i <= 100; i++) {
        for (int j = -100; j <= 100; j++) {
            if (i * j == a * c && i + j == b) {
                printf("Roots are: %d/%d and %d/%d\n", -j, a, -i, a);
                found = 1;
                break;
            }
        }
        if (found) break;
    }
    if (!found) printf("Cannot be factorized easily.\n");
}

int main() {
    int a, b, c;
    printf("Enter coefficients a, b, and c: ");
    scanf("%d %d %d", &a, &b, &c);
    findRootsByFactorization(a, b, c);
    return 0;
}
            

Method 3: Using Recursion

This method recursively calculates the discriminant and finds the roots.

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


void findRootsRecursive(int a, int b, int c, float d) {
    if (d > 0) {
        float root1 = (-b + sqrt(d)) / (2 * a);
        float root2 = (-b - sqrt(d)) / (2 * a);
        printf("Real and Distinct Roots: %.2f, %.2f\n", root1, root2);
    } else if (d == 0) {
        float root = -b / (2 * a);
        printf("Real and Equal Roots: %.2f\n", root);
    } else {
        float realPart = -b / (2 * a);
        float imagPart = sqrt(-d) / (2 * a);
        printf("Complex Roots: %.2f + %.2fi, %.2f - %.2fi\n", realPart, imagPart, realPart, imagPart);
    }
}

void calculateDiscriminant(int a, int b, int c) {
    float d = b * b - 4 * a * c;
    findRootsRecursive(a, b, c, d);
}

int main() {
    int a, b, c;
    printf("Enter coefficients a, b, and c: ");
    scanf("%d %d %d", &a, &b, &c);
    calculateDiscriminant(a, b, c);
    return 0;
}