### Program 18:To find roots of quadratic equation

Program 18:
```#include<stdio.h>
#include<stdlib.h>
#include<math.h>
int main()
{
float A, B, C, root1, root2;
float real, imaginary, discriminant;
printf("Enter the values of A, B and C\n");
scanf("%f %f %f", &A,&B,&C);
if( A==0 || B==0 || C==0)
{
printf("Error: Roots cannot be determined\n");
}
else
{
discriminant = B*B - 4.0*A*C;
if(discriminant < 0)
{
printf("Imaginary Roots\n");
real = -B/(2.0*A) ;
imaginary = sqrt(abs(discriminant))/(2.0*A);
printf("Root1 = %f +i %f\n",real, imaginary);
printf("Root2 = %f -i %f\n",real, imaginary);
}
else if(discriminant == 0)
{
printf("Roots are real and equal\n");
root1 = -B/(2.0*A);
root2 = root1;
printf("Root1 = %f \n",root1);
printf("Root2 = %f \n",root2);
}
else if(discriminant > 0 )
{
printf("Roots are real and distinct\n");
root1 =(-B+sqrt(discriminant))/(2.0*A);
root2 =(-B-sqrt(discriminant))/(2.0*A);
printf("Root1 = %f \n",root1);
printf("Root2 = %f \n",root2);
}
}
return 0;
}```
Explanation:
1. As you know a quadratic equation is ax2+bx+c
2. The program starts with initilizing
• A-for storing value of a as in ax2+bx+c
• B-for storing value of b as in ax2+bx+c
• C-for storing value of c as in ax2+bx+c
3. Checking whether all values are 0 or not and if any one of them is zero then it will
• print an error message saying roots can't be determined.
4. If step 3 is not satisfied then
• we should calculate discriminant by using formula (d=b2-4ac)
• If discriminant is less than zero
• There are no real roots and all are imaginary
• real part is calculated by using formula real=-b/2a
• imaginary part is calculated by formula imaginary=√|d|/2a
• Then printing roots of equation.
• If discriminant is equal to zero then the roots are Real and Equal
• roots are calculated by using formula root=-b/2a for both
• Then printing roots of equation.
• If discriminant is greater than zero then the Roots are real and distinct
• root1 is calculated by using formula root1=(-b+√|d|/2a)/2a
• root2 is calculated by formula root2=(-b-√|d|/2a)/2a
• Then printing roots of equation.

Output: