13.C program to Find all Roots of a Quadratic equation

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 determinant).

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

• C Programming Operators
• C if, if...else and Nested if...else Statement

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 determinant of a quadratic equation. The determinant tells the nature of the roots.

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

Example: Program to Find Roots of a Quadratic Equation

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

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

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

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

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

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

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

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

    // if roots are not real 
    else
    {
        realPart = -b/(2*a);
        imaginaryPart = sqrt(-determinant)/(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.

Check out these related examples:

• C Program to Add Two Complex Numbers by Passing Structure to a Function
• C Program to Calculate Standard Deviation
• C Program to Find the Largest Number Among Three Numbers