This Quadratic formula is used only when b²– 4ac >= 0. such that, If b²– 4ac > 0 , means the equation has more than one real roots if b²– 4ac = 0 , means equal or single root if b²– 4ac <0, i3mplies imaginary root Lastly, if a is 0, then the equation would not be counted as a quadratic equation.

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

Program

Check out “Quadratic Equation” program along with its tested test cases.

Robustness Testing

We are assuming interval [0,10] where our input values will come in between and we will create test cases using Robustness testing accordingly.

In Robustness Testing, it will produce 6N+1 test cases which means, in this case, there will be 6*3+1 = 19 test cases.

How it is different from Boundary Value Analysis?

We can observe that previously we didn’t check for input values higher than the maximum boundary limit and lesser than the minimum boundary limit. In other words, we haven’t tested our code for Invalid Inputs in Boundary Value Analysis but in Robustness testing, we did make test cases for invalid inputs too and rewrite the code to fulfill this condition.

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