Skip to main content

Boundary Value Analysis : Nature of Roots of a Quadratic equation

Consider a problem for the determination of the nature of the roots of a quadratic equation where the inputs are 3 variables (a, b, c) and their values may be from the interval [0, 100]. The output may be one of the following depending on the values of the variables:

  • Not a quadratic equation,
  • Real roots,
  • Imaginary roots,
  • Equal roots

Our objective is to design the boundary value test cases. Boundary value analysis is a software testing technique in which tests are designed to include representatives of boundary values in a range. A boundary value analysis has a total of 4*n+1 distinct test cases, where n is the number of variables in a problem. Here we have to consider all three variables and design all the distinct possible test cases. We will have a total of 13 test cases as n = 3.

  • Roots are real if (b2 – 4ac) > 0
  • Roots are imaginary if (b2 – 4ac) < 0
  • Roots are equal if (b2 – 4ac) = 0
  • Equation is not quadratic if a = 0

How do we design the test cases ? For each variable we consider below 5 cases:

  • amin = 0
  • amin+1 = 1
  • anominal = 50
  • amax-1 = 99
  • amax = 100

When we are considering these 5 cases for a variable, rest of the variables have the nominal values, like in the above case where the value of ‘a’ is varying from 0 to 100, the value of ‘b’ and ‘c’ will be taken as the nominal or average value. Similarly, when the values of variable ‘b’ are changing from 0 to 100, the values of ‘a’ and ‘c’ will be nominal or average i.e 50. The possible test cases for the nature of roots of a Quadratic Equation in a Boundary Value Analysis can be: Below is the program that verifies the test cases considered in the table shown above. The program takes user-defined inputs so that you can check for any of the test cases mentioned above. 

C++




// C++ program to check the nature of the roots
 
#include
using namespace std;
 
// BVA for nature of roots of a quadratic equation
void nature_of_roots(int a, int b, int c)
 
    // If a = 0, D/2a will yield exception
    // Hence it is not a valid Quadratic Equation
    if (a == 0)
        cout << "Not a Quadratic Equation"
             << endl;
        return;
    
 
    int D = b * b - 4 * a * c;
 
    // If D > 0, it will be Real Roots
    if (D > 0)
        cout << "Real Roots" << endl;
    
 
    // If D == 0, it will be Equal Roots
    else if (D == 0)
        cout << "Equal Roots" << endl;
    
 
    // If D < 0, it will be Imaginary Roots
    else
        cout << "Imaginary Roots" << endl;
    
 
// Function to check for all testcases
void checkForAllTestCase()
 
    cout << "Testcase"
         << "\ta\tb\tc\tActual Output"
         << endl;
    cout << endl;
    int a, b, c;
    int testcase = 1;
    while (testcase <= 13)
        if (testcase == 1)
            a = 0;
            b = 50;
            c = 50;
        
        else if (testcase == 2)
            a = 1;
            b = 50;
            c = 50;
        
        else if (testcase == 3)
            a = 50;
            b = 50;
            c = 50;
        
        else if (testcase == 4)
            a = 99;
            b = 50;
            c = 50;
        
        else if (testcase == 5)
            a = 100;
            b = 50;
            c = 50;
        
        else if (testcase == 6)
            a = 50;
            b = 0;
            c = 50;
        
        else if (testcase == 7)
            a = 50;
            b = 1;
            c = 50;
        
        else if (testcase == 8)
            a = 50;
            b = 99;
            c = 50;
        
        else if (testcase == 9)
            a = 50;
            b = 100;
            c = 50;
        
        else if (testcase == 10)
            a = 50;
            b = 50;
            c = 0;
        
        else if (testcase == 11)
            a = 50;
            b = 50;
            c = 1;
        
        else if (testcase == 12)
            a = 50;
            b = 50;
            c = 99;
        
        else if (testcase == 13)
            a = 50;
            b = 50;
            c = 100;
        
        cout << "\t" << testcase << "\t"
             << a << "\t" << b << "\t"
             << c << "\t";
        nature_of_roots(a, b, c);
        cout << endl;
        testcase++;
    
 
// Driver Code
int main()
    checkForAllTestCase();
    return 0;
 















Java

















 






 




 



























// Java program to check the nature of the roots


import java.util.*;


 


class GFG




 


// BVA for nature of roots of a quadratic equation


static void nature_of_roots(int a, int b, int c)




 


    // If a = 0, D/2a will yield exception


    // Hence it is not a valid Quadratic Equation


    if (a == 0)


    


        System.out.print("Not a Quadratic Equation"


            +"\n");


        return;


    


 


    int D = b * b - 4 * a * c;


 


    // If D > 0, it will be Real Roots


    if (D > 0) 


        System.out.print("Real Roots" +"\n");


    


 


    // If D == 0, it will be Equal Roots


    else if (D == 0) 


        System.out.print("Equal Roots" +"\n");


    


 


    // If D < 0, it will be Imaginary Roots


    else 


        System.out.print("Imaginary Roots" +"\n");


    




 


// Function to check for all testcases


static void checkForAllTestCase()




 


    System.out.print("Testcase"


        + "\ta\tb\tc\tActual Output"


        +"\n");


    System.out.println();


    int a, b, c;


    a = b = c = 0;


    int testcase = 1;


    while (testcase <= 13) 


        if (testcase == 1) 


            a = 0;


            b = 50;


            c = 50;


        


        else if (testcase == 2) 


            a = 1;


            b = 50;


            c = 50;


        


        else if (testcase == 3) 


            a = 50;


            b = 50;


            c = 50;


        


        else if (testcase == 4) 


            a = 99;


            b = 50;


            c = 50;


        


        else if (testcase == 5) 


            a = 100;


            b = 50;


            c = 50;


        


        else if (testcase == 6) 


            a = 50;


            b = 0;


            c = 50;


        


        else if (testcase == 7) 


            a = 50;


            b = 1;


            c = 50;


        


        else if (testcase == 8) 


            a = 50;


            b = 99;


            c = 50;


        


        else if (testcase == 9) 


            a = 50;


            b = 100;


            c = 50;


        


        else if (testcase == 10) 


            a = 50;


            b = 50;


            c = 0;


        


        else if (testcase == 11) 


            a = 50;


            b = 50;


            c = 1;


        


        else if (testcase == 12) 


            a = 50;


            b = 50;


            c = 99;


        


        else if (testcase == 13) 


            a = 50;


            b = 50;


            c = 100;


        


        System.out.print("\t" + testcase+ "\t"


            + a+ "\t" + b+ "\t"


            + c+ "\t");


        nature_of_roots(a, b, c);


        System.out.println();


        testcase++;


    




 


// Driver Code


public static void main(String[] args)




    checkForAllTestCase();






 


// This code is contributed by 29AjayKumar






































Python3

















 






 




 



























# Python3 program to check the nature of the roots


 


# BVA for nature of roots of a quadratic equation


def nature_of_roots(a, b, c):


 


    # If a = 0, D/2a will yield exception


    # Hence it is not a valid Quadratic Equation


    if (a == 0):


        print("Not a Quadratic Equation");


        return;


     


    D = b * b - 4 * a * c;


 


    # If D > 0, it will be Real Roots


    if (D > 0):


        print("Real Roots");


     


    # If D == 0, it will be Equal Roots


    elif(D == 0):


        print("Equal Roots");


     


    # If D < 0, it will be Imaginary Roots


    else:


        print("Imaginary Roots");


     


# Function to check for all testcases


def checkForAllTestCase():


 


    print("Testcase\ta\tb\tc\tActual Output");


    print();


    a = b = c = 0;


    testcase = 1;


    while (testcase <= 13):


        if (testcase == 1):


            a = 0;


            b = 50;


            c = 50;


        elif(testcase == 2):


            a = 1;


            b = 50;


            c = 50;


        elif(testcase == 3):


            a = 50;


            b = 50;


            c = 50;


        elif(testcase == 4):


            a = 99;


            b = 50;


            c = 50;


        elif(testcase == 5):


            a = 100;


            b = 50;


            c = 50;


        elif(testcase == 6):


            a = 50;


            b = 0;


            c = 50;


        elif(testcase == 7):


            a = 50;


            b = 1;


            c = 50;


        elif(testcase == 8):


            a = 50;


            b = 99;


            c = 50;


        elif(testcase == 9):


            a = 50;


            b = 100;


            c = 50;


        elif(testcase == 10):


            a = 50;


            b = 50;


            c = 0;


        elif(testcase == 11):


            a = 50;


            b = 50;


            c = 1;


        elif(testcase == 12):


            a = 50;


            b = 50;


            c = 99;


        elif(testcase == 13):


            a = 50;


            b = 50;


            c = 100;


         


        print("\t" , testcase , "\t" , a , "\t" , b , "\t" , c , "\t", end="");


        nature_of_roots(a, b, c);


        print();


        testcase += 1;


     


# Driver Code


if __name__ == '__main__':


    checkForAllTestCase();


 


# This code is contributed by 29AjayKumar






































C#

















 






 




 



























// C# program to check the nature of the roots


using System;


 


class GFG




 


// BVA for nature of roots of a quadratic equation


static void nature_of_roots(int a, int b, int c)




 


    // If a = 0, D/2a will yield exception


    // Hence it is not a valid Quadratic Equation


    if (a == 0)


    


        Console.Write("Not a Quadratic Equation"


                       +"\n");


        return;


    


 


    int D = b * b - 4 * a * c;


 


    // If D > 0, it will be Real Roots


    if (D > 0) 


        Console.Write("Real Roots" +"\n");


    


 


    // If D == 0, it will be Equal Roots


    else if (D == 0) 


        Console.Write("Equal Roots" +"\n");


    


 


    // If D < 0, it will be Imaginary Roots


    else 


        Console.Write("Imaginary Roots" +"\n");


    




 


// Function to check for all testcases


static void checkForAllTestCase()




 


    Console.Write("Testcase"


        + "\ta\tb\tc\tActual Output"


        +"\n");


    Console.WriteLine();


    int a, b, c;


    a = b = c = 0;


    int testcase = 1;


    while (testcase <= 13) 


        if (testcase == 1) 


            a = 0;


            b = 50;


            c = 50;


        


        else if (testcase == 2) 


            a = 1;


            b = 50;


            c = 50;


        


        else if (testcase == 3) 


            a = 50;


            b = 50;


            c = 50;


        


        else if (testcase == 4) 


            a = 99;


            b = 50;


            c = 50;


        


        else if (testcase == 5) 


            a = 100;


            b = 50;


            c = 50;


        


        else if (testcase == 6) 


            a = 50;


            b = 0;


            c = 50;


        


        else if (testcase == 7) 


            a = 50;


            b = 1;


            c = 50;


        


        else if (testcase == 8) 


            a = 50;


            b = 99;


            c = 50;


        


        else if (testcase == 9) 


            a = 50;


            b = 100;


            c = 50;


        


        else if (testcase == 10) 


            a = 50;


            b = 50;


            c = 0;


        


        else if (testcase == 11) 


            a = 50;


            b = 50;


            c = 1;


        


        else if (testcase == 12) 


            a = 50;


            b = 50;


            c = 99;


        


        else if (testcase == 13) 


            a = 50;


            b = 50;


            c = 100;


        


        Console.Write("\t" + testcase+ "\t"


                        + a+ "\t" + b+ "\t"


                        + c+ "\t");


        nature_of_roots(a, b, c);


        Console.WriteLine();


        testcase++;


    




 


// Driver Code


public static void Main(String[] args)




    checkForAllTestCase();






 


// This code is contributed by 29AjayKumar






































Javascript

















 






 




 



























// JavaScript program to check the nature of the roots


 


 


// BVA for nature of roots of a quadratic equation


function nature_of_roots(a, b, c)




 


    // If a = 0, D/2a will yield exception


    // Hence it is not a valid Quadratic Equation


    if (a == 0) 


        console.log("Not a Quadratic Equation")


        return;


    


 


    let D = b * b - 4 * a * c;


 


    // If D > 0, it will be Real Roots


    if (D > 0) 


        console.log("Real Roots");


    


 


    // If D == 0, it will be Equal Roots


    else if (D == 0) 


        console.log("Equal Roots");


    


 


    // If D < 0, it will be Imaginary Roots


    else 


        console.log("Imaginary Roots");


    




 


// Function to check for all testcases


function checkForAllTestCase()




 


    console.log("Testcase\ta\tb\tc\tActual Output\n");


    let a, b, c;


    let testcase = 1;


    while (testcase <= 13) 


        if (testcase == 1) 


            a = 0;


            b = 50;


            c = 50;


        


        else if (testcase == 2) 


            a = 1;


            b = 50;


            c = 50;


        


        else if (testcase == 3) 


            a = 50;


            b = 50;


            c = 50;


        


        else if (testcase == 4) 


            a = 99;


            b = 50;


            c = 50;


        


        else if (testcase == 5) 


            a = 100;


            b = 50;


            c = 50;


        


        else if (testcase == 6) 


            a = 50;


            b = 0;


            c = 50;


        


        else if (testcase == 7) 


            a = 50;


            b = 1;


            c = 50;


        


        else if (testcase == 8) 


            a = 50;


            b = 99;


            c = 50;


        


        else if (testcase == 9) 


            a = 50;


            b = 100;


            c = 50;


        


        else if (testcase == 10) 


            a = 50;


            b = 50;


            c = 0;


        


        else if (testcase == 11) 


            a = 50;


            b = 50;


            c = 1;


        


        else if (testcase == 12) 


            a = 50;


            b = 50;


            c = 99;


        


        else if (testcase == 13) 


            a = 50;


            b = 50;


            c = 100;


        


        process.stdout.write("\ttestcase\t" + a + "\t" + b + "\t" + c + "\t");


        nature_of_roots(a, b, c);


        testcase++;


    




 


// Driver Code


checkForAllTestCase();


 


 


// This code is contributed bt phasing17








































Output:

Testcase    a    b    c    Actual Output

    1    0    50    50    Not a Quadratic Equation

    2    1    50    50    Real Roots

    3    50    50    50    Imaginary Roots

    4    99    50    50    Imaginary Roots

    5    100    50    50    Imaginary Roots

    6    50    0    50    Imaginary Roots

    7    50    1    50    Imaginary Roots

    8    50    99    50    Imaginary Roots

    9    50    100    50    Equal Roots

    10    50    50    0    Real Roots

    11    50    50    1    Real Roots

    12    50    50    99    Imaginary Roots

    13    50    50    100    Imaginary Roots




Time complexity: O(1)
Auxiliary space: O(1)








                                            Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.

                                            Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!







 

https://neveropen.tech/boundary-value-analysis-nature-of-roots-of-a-quadratic-equation/?feed_id=14&_unique_id=683ca4eee7055












Labels:





























Comments











Post a Comment



















Popular posts from this blog





















Bare Metal Billing Client Portal Guide




























      Contents   Order a Bare Metal Server  My Custom / Contract Pricing   View Contract Details   Location Management      Order History & Status   View Order Details         Introduction  The phoenixNAP Client Portal allows you to purchase bare metal servers  and other phoenixNAP products and services. Using the intuitive interface and its essential tools, you can also easily manage your infrastructure.  This quick guide will show you how to use the new form  to order a bare metal server and how to navigate through new bare metal features  within the phoenixNAP Client Portal.     Order a Bare Metal Server  An order form is an accordion-based process for purchasing phoenixNAP products. Our order form allows you to view the pricing and order multiple products from the same category at the same time.     Note:  The prices on the form are per month . A contract is not required. However, if you want a contracted price, you may be eligible for a discount  depending on the quantity and ...




















Post a Comment









Read more






























Add an element in Array  to make the bitwise XOR as K




























   Given an array arr[]  containing N positive integers, the task is to add an integer such that the bitwise Xor of the new array becomes K.  Examples:    Input: arr[] = 1, 4, 5, 6, K = 4 Output: 2 Explanation: Bit-wise XOR of the array is 6.  And bit-wise XOR of 6 and 2 is 4.  Input: arr[] = 2, 7, 9, 1, K = 5 Output:  8        Approach: The solution to the problem is based on the following idea of bitwise Xor:   If for two numbers X  and Y , the bitwise Xor of X and Y is Z  then the bitwise Xor of X and Z is Y.   Follow the steps to solve the problem:   Let the bitwise XOR of the array elements be X .   Say the required value to be added is Y  such that X Xor Y = K .  From the above observation, it is clear that the value to be added (Y) is the same as X Xor K .   Below is the implementation of the above approach:   C++                                 // C++ code to implement the above approach     #include  using  namespace  std;     // Function to find the required value  int  find_...




















Post a Comment









Read more






























Mahotas – Template Matching




























   In this article we will see how we can do template matching in mahotas. Template is basically a part or structure of image. In this tutorial we will use “lena” image, below is the command to load it.    mahotas.demos.load('lena')  Below is the lena image             In order to do this we will use mahotas.template_match method Syntax :  mahotas.template_match(img, template) Argument :  It takes image object and template as argument Return :  It returns image object      Note :  Input image should be filtered or should be loaded as grey In order to filter the image we will take the image object which is numpy.ndarray and filter it with the help of indexing, below is the command to do this    image = image[:, :, 0]  Below is the implementation        Python3                                 # importing required libraries  import  mahotas  import  mahotas.demos  from  pylab import  gray, imshow, show  import  numpy as np  import  matplotlib.pyplot as plt        # loading image  ...




















Post a Comment









Read more