Roots of a quadratic equation

Posted on Apr 17, 2020

C program to find out the roots of a quadratic equation a*x*x + b*x + c = 0, where a, b, and c are entered by the user.

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. It tells the nature of the roots.

If the discriminant is greater than 0, the roots are real and different.

If the discriminant is equal to 0, the roots are real and equal.

If the discriminant is less than 0, the roots are complex (imaginary) and different.

Program

#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
#include<math.h>
void main()
{
	float a, b, c;
    float disc, root1, root2;
    float temp1, temp2;

    printf("\nEnter the values of a,b,c\t:");
    scanf("%f%f%f",&a,&b,&c);

    if(a==0)
    {
		printf("\nThe equation is linear and not quadratic");
		getch();
		exit(0);
    }

    disc = (b * b) - (4 * a * c);
    if(disc < 0)
    {
		temp1= ((-1) * b) / (2 * a);
		temp2= (sqrt((-1) * disc)) / (2 * a);
		printf("\nEquation has imaginary roots and are\n1. %.2f + i%.2f\n2. %.2f - i%.2f",temp1,temp2,temp1,temp2);
    }
    else if(disc == 0)
    {
		root1 = ((-1) * b) / (2 * a);
		root2 = root1;
		printf("\nThe roots are equal and are\n1. %.2f\n2. %.2f",root1,root2);
    }
    else if(disc > 0)
    {
		root1 = (((-1) * b) + sqrt(disc)) / (2 * a);
		root2 = (((-1) * b) - sqrt(disc)) / (2 * a);
		printf("\nThe roots are real and are\n1. %.2f\n2. %.2f",root1,root2);
    }

    getch();
}

Output

********** Run1 ********** 

Enter the values of a,b,c       :1
2
1

The roots are equal and are
1. -1.00
2. -1.00


********** Run2 ********** 

Enter the values of a,b,c       :2
6
2

The roots are real and are
1. -0.38
2. -2.62


********** Run3 ********** 

Enter the values of a,b,c       :1
1
1

Equation has imaginary roots and are
1. -0.50 + i0.87
2. -0.50 - i0.87


********** Run4 ********** 

Enter the values of a,b,c       :0
3
4

The equation is linear and not quadratic

Explanation