Introduction

Quadratic equations are a fundamental concept in algebra, typically represented in the form:

ax² + bx + c = 0

Where a, b, and c are constants, and x represents the variable.

Objective

The objective of this program is to solve quadratic equations by calculating the roots using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Given values for a, b, and c, this C program will determine if the equation has real roots or complex roots, and will then display the appropriate roots.

Code

#include 
#include 

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

    // Taking input for a, b, and c
    printf("Enter coefficients a, b, and c: ");
    scanf("%f %f %f", &a, &b, &c);

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

    // Checking if the discriminant is positive, negative, or zero
    if (discriminant > 0) {
        // Two real and distinct roots
        root1 = (-b + sqrt(discriminant)) / (2 * a);
        root2 = (-b - sqrt(discriminant)) / (2 * a);
        printf("The roots are real and distinct: %.2f and %.2f\n", root1, root2);
    } 
    else if (discriminant == 0) {
        // One real root
        root1 = -b / (2 * a);
        printf("The root is real and the same: %.2f\n", root1);
    } 
    else {
        // Complex roots
        float realPart = -b / (2 * a);
        float imaginaryPart = sqrt(-discriminant) / (2 * a);
        printf("The roots are complex:\n");
        printf("Root 1 = %.2f + %.2fi\n", realPart, imaginaryPart);
        printf("Root 2 = %.2f - %.2fi\n", realPart, imaginaryPart);
    }

    return 0;
}

Program Explanation

This C program solves a quadratic equation using the following steps:

• Input: The program asks the user to enter values for the coefficients a, b, and c.
• Discriminant Calculation: The discriminant D = b² – 4ac is calculated. The discriminant helps determine the nature of the roots.
• Root Calculation: Based on the value of the discriminant:
  • If D > 0, the equation has two real and distinct roots.
  • If D = 0, the equation has one real root.
  • If D < 0, the equation has complex (imaginary) roots.
• Output: The program prints the roots of the equation to the screen based on the discriminant’s value.

How to Run the Program

1. 1. Open a C programming environment or a code editor like Code::Blocks, Dev-C++, or an IDE like Visual Studio.
   2. Create a new C file and paste the provided code into the file.
   3. Save the file with a .c extension (e.g., quadratic_solver.c).
   4. Compile the code using the built-in compiler in your IDE or by using a command line compiler like gcc:

gcc quadratic_solver.c -o quadratic_solver

1. Run the program and input values for a, b, and c when prompted.
2. The program will output the roots of the quadratic equation.