This Quadratic formula is applied only when b²– 4ac >= 0.
such that,
If b²– 4ac > 0 , means the eqn. has more than one real roots
if b²– 4ac = 0 , represent equal or single root
if b²– 4ac <0, represents imaginary root
Lastly, if a is 0, then the equation would not be considered as a quadratic equation.

So, a quadratic equation can have [ Real, Equal, Imaginary, not quadratic ]

We are supposing interval [0,10] where our input values will fall in between this interval and we will create test cases using Boundary Value Analysis accordingly.

Program:

#include<conio.h>
#include<stdio.h>
#include<math.h>
void main()
{
float a,b,c,result;
printf(" ax^2 + bx + c, \n enter the values of a, b and c : = ");
scanf("%f %f %f", &a,&b,&c);

result = (b*b)- (4*a*c);
if(a==0)
printf("not quadratic");
else if(result>0)
{
result= sqrt(result);
printf("Real roots are, %f,%f \n",(-b-result)/(2*a),(-b+result)/(2*a));
}
else if(result==0)
{
result= sqrt(result);
printf("equal root, %f,%f \n",(-b)/(2*a),(-b)/(2*a));
}
else
{
printf("Imaginary root");
}

getch();
}

Testing the Program

Real roots:

  

Equal roots:

Not Quadratic

Imaginary :

In Boundary Value Analysis, there will be 4N+1 test cases which means 4*3+1 = 13 test cases will be generated 

Test ID	a	b	c	Expected Output	Program Output	Tested Outcome
1	0	5	5	Not Quadratic	Not Quadratic	Pass
2	1	5	5	Real	Real	Pass
3	9	5	5	Imaginary	Imaginary	Pass
4	10	5	5	Imaginary	Imaginary	Pass
5	5	0	5	Imaginary	Imaginary	Pass
6	5	1	5	Imaginary	Imaginary	Pass
7	5	9	5	Imaginary	Imaginary	Pass
8	5	10	5	Equal	Equal	Pass
9	5	5	0	Real	Real	Pass
10	5	5	1	Real	Real	Pass
11	5	5	9	Imaginary	Imaginary	Pass
12	5	5	10	Imaginary	Imaginary	Pass
13	5	5	5	Imaginary	Imaginary	Pass