Roots Of A Quadratic Equation

December 12, 2020

Finding Roots of a Quadratic Equation

In this C program, we will find the roots of a quadratic equation [ax2 + bx + c]. We can solve a Quadratic Equation by finding its roots. Mainly roots of the quadratic equation are represented by a parabola in 3 different patterns like :

  • No Real Roots
  • One Real Root
  • Two Real Roots

We get the roots of the equation which satisfies any one of the above conditions :
X = [-b (+or-)[Squareroot(pow(b,2)-4ac)]]/2a

Sample Test Case

Enter value of a :1
Enter value of b :-7
Enter value of c :12
Output
Two Real Roots
4.0
3.0

Finding Roots of a Quadratic Equation using C

Algorithm

  1. Start.
  2. Take input from user a,b,c.
  3. Check the value of a i.e. a!=0.
  4. Calculate Discriminant (D)
    • D = b^2 – 4*a*c
  5. If D>0 : Two real root exists.
  6. If D=0 : Equal root exists.
  7. If D<0 : Imaginary root exists.
  8. Display the existence of roots and the roots of the equation.
  9. End.

C Code

#include <math.h>
#include <stdio.h>
int main() {
    double a, b, c, d, root1, root2, r, i;
    printf(“Enter value of a, b and c: “);
    scanf(“%lf %lf %lf”, &a, &b, &c);

    d = b * b – 4 * a * c;

    // condition for real and different roots
    if (d > 0) {
        printf(“Two Real Roots\n“);
        root1 = (-b + sqrt(d)) / (2 * a);
        root2 = (-b – sqrt(d)) / (2 * a);
        printf(“root1 = %.2lf \nroot2 = %.2lf”, root1, root2);
    }

    // condition for real and equal roots
    else if (d == 0) {
        printf(“Equal Roots\n“);
        root1 = root2 = –b / (2 * a);
        printf(“root1 = root2 = %.2lf;”, root1);
    }

    // if roots are not real
    else {
        r = –b / (2 * a);
        i = sqrt(-d) / (2 * a);
        printf(“No Real Roots\n“);
        printf(“root1 = %.2lf+%.2lfi \nroot2 = %.2f-%.2fi”, r, i, r, i);
    }

    return 0;
} 

Output

Enter value of a, b and c: 1 –7 12    
                                                                                                         
Two Real Roots                                                                                                                                 
root1 = 4.00                                                                                                                                   
root2 = 3.00
 

This page is contributed by Rishav Raj