C program to find all roots of a quadratic equation

Quadratic equations play a fundamental role in mathematics and science, representing a key concept in algebra. In this article, we'll explore how to create a simple C program to find all roots of a quadratic equation.

Understanding Quadratic Equations

A quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants and x represents the variable. The roots of a quadratic equation are the values of x that satisfy the equation.

C program to find all roots of a quadratic equation

Let's delve into the C programming language to create a program that calculates all roots of a quadratic equation using the quadratic formula.

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

int main() {
    float a, b, c;
    float discriminant, root1, root2, realPart, imaginaryPart;

    // Input from the user
    printf("Enter coefficients (a, b, c): ");
    scanf("%f %f %f", &a, &b, &c);

    // Calculating discriminant
    discriminant = b * b - 4 * a * c;

    // Checking conditions to find roots
    if (discriminant > 0) {
        // Real and different roots
        root1 = (-b + sqrt(discriminant)) / (2 * a);
        root2 = (-b - sqrt(discriminant)) / (2 * a);
        printf("Roots are real and different: %.2f and %.2f", root1, root2);
    } else if (discriminant == 0) {
        // Real and equal roots
        root1 = root2 = -b / (2 * a);
        printf("Roots are real and equal: %.2f and %.2f", root1, root2);
    } else {
        // Complex roots
        realPart = -b / (2 * a);
        imaginaryPart = sqrt(-discriminant) / (2 * a);
        printf("Roots are complex and different: %.2f + %.2fi and %.2f - %.2fi", realPart, imaginaryPart, realPart, imaginaryPart);
    }

    return 0;
}

Output

Enter coefficients (a, b, c): 1 -3 2
Roots are real and different: 2.00 and 1.00

Enter coefficients (a, b, c): 1 2 1
Roots are real and equal: -1.00 and -1.00

Enter coefficients (a, b, c): 1 1 1
Roots are complex and different: -0.50 + 0.87i and -0.50 - 0.87i

Understanding the Code

1. User Input: The user is prompted to enter coefficients (a, b, and c) of the quadratic equation using scanf().
2. Calculating Discriminant: The program calculates the discriminant (b^2 - 4ac), which determines the nature of roots.
3. Finding Roots: Based on the value of the discriminant, the program identifies and computes the roots using conditional statements.

In this article, we've created a simple C program that efficiently finds all roots of a quadratic equation using the quadratic formula. Understanding the discriminant and employing conditional checks through C programming allows us to compute real, equal, or complex roots accurately.