C Program to Find all Roots of a Quadratic Equation

This program accepts coefficients of a quadratic equation from the user and displays the roots (both real and complex roots depending upon the discriminant ).
Quadratic equation graph

To understand this example, you should have the knowledge of following C programming topics:

The standard form of a quadratic equation is:

ax2 + bx + c = 0, where
a, b and c are real numbers and
a ≠ 0

The term b2-4ac is known as the discriminant of a quadratic equation. The discriminant tells the nature of the roots.

  • If discriminant is greater than 0, the roots are real and different.
  • If discriminant is equal to 0, the roots are real and equal.
  • If discriminant is less than 0, the roots are complex and different.

Discriminant of quadratic equation

Example: Program to Find Roots of a Quadratic Equation


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

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

    printf("Enter coefficients a, b and c: ");
    scanf("%lf %lf %lf",&a, &b, &c);

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

    // condition for real and different roots
    if (discriminant > 0)
    {
    // sqrt() function returns square root
        root1 = (-b+sqrt(discriminant))/(2*a);
        root2 = (-b-sqrt(discriminant))/(2*a);

        printf("root1 = %.2lf and root2 = %.2lf",root1 , root2);
    }

    //condition for real and equal roots
    else if (discriminant == 0)
    {
        root1 = root2 = -b/(2*a);

        printf("root1 = root2 = %.2lf;", root1);
    }

    // if roots are not real 
    else
    {
        realPart = -b/(2*a);
        imaginaryPart = sqrt(-discriminant)/(2*a);
        printf("root1 = %.2lf+%.2lfi and root2 = %.2f-%.2fi", realPart, imaginaryPart, realPart, imaginaryPart);
    }

    return 0;
}   

Output 

Enter coefficients a, b and c: 2.3
4
5.6
Roots are: -0.87+1.30i and -0.87-1.30i

In this program, library function sqrt() is used to find the square root of a number. To learn more, visit:  sqrt() function.