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Decision Making Programs in C

Find roots of quadratic equation

Introduction

A quadratic equation is in the form:

ax2+bx+c=0

where

  • a, b, and c are real numbers
  • a ≠ 0

The roots of the equation are given by the quadratic formula:

x = (−b±sqrt(b2−4ac))/2a 

The discriminant DDD helps determine the nature of the roots:

D=b2−4ac

  • If D>0 → Two distinct real roots
  • If D=0 → Two equal real roots
  • If D<0 → Complex conjugate roots

 

C Program: Find Roots of Quadratic Equation

C 
#include <stdio.h>


#include <math.h>


 


int main() {


    float a, b, c, discriminant, root1, root2, realPart, imagPart;


 


    // Input coefficients


    printf("Enter coefficients a, b and c: ");


    scanf("%f %f %f", &a, &b, &c);


 


    // Calculate discriminant


    discriminant = b * b - 4 * a * c;


 


    // Check the nature of roots


    if (discriminant > 0) {


        // Real and distinct roots


        root1 = (-b + sqrt(discriminant)) / (2 * a);


        root2 = (-b - sqrt(discriminant)) / (2 * a);


        printf("Roots are real and different.\n");


        printf("Root 1 = %.2f\n", root1);


        printf("Root 2 = %.2f\n", root2);


    }


    else if (discriminant == 0) {


        // Real and equal roots


        root1 = root2 = -b / (2 * a);


        printf("Roots are real and equal.\n");


        printf("Root 1 = Root 2 = %.2f\n", root1);


    }


    else {


        // Complex roots


        realPart = -b / (2 * a);


        imagPart = sqrt(-discriminant) / (2 * a);


        printf("Roots are complex and conjugate.\n");


        printf("Root 1 = %.2f + %.2fi\n", realPart, imagPart);


        printf("Root 2 = %.2f - %.2fi\n", realPart, imagPart);


    }


 


    return 0;


}

Output

 
OUTPUT 1 :
Enter coefficients a, b and c: 1 5 6
Roots are real and different.
Root 1 = -2.00
Root 2 = -3.00

OUTPUT 2 :
Enter coefficients a, b and c: 1 4 4
Roots are real and equal.
Root 1 = Root 2 = -2.00

OUTPUT 3 :
Enter coefficients a, b and c: 1 2 5
Roots are complex and conjugate.
Root 1 = -1.00 + 2.00i
Root 2 = -1.00 - 2.00i

Explanation

  1. User inputs a, b, and c.
  2. The discriminant D = b² - 4ac is calculated.
  3. Depending on the value of D:
    • If positive → two distinct real roots.
    • If zero → two equal real roots.
    • If negative → complex conjugate roots.
  4. The roots are printed accordingly.

 

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