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

Algorithm

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

Prepinsta Prime