Question

A quadratic equation is generally represented as,

ax^2 + bx + c

The root(s) of the above quadratic equation is computed using the following formula,

root1 = (-b + sqrt(D))/ 2a
root2 = (-b - sqrt(D))/2a

Where D is the discriminant of the quadratic equation and is computed as,
D = b^2 - 4ac

Given the value of D, the roots of a quadratic equation can be categorized as follows,
D > 0 : Two distinct real roots
D = 0 : Two equal real roots
D < 0 : Two distinct complex roots

WAP in C++ to develop a quadratic equation solver using functions. The users will input the values of a, b, and c. Your program must validate that the value of a is not equal to zero (If the input is invalid, user should be prompted an error message and asked to renter only the invalid input). Functions should be written to carry out
a. the input process
b. validate the inputs
c. solve the equation
d. the output process

Also note that all of the above functions, with the exception of validate function (bullet "b") should be coded using "call by reference" method. You are free to use any other function you might need/want (call by value or call by reference).

Output should have the information on what type of roots (two real distinct, two real equal or two complex distinct) and the values of the roots. In this regard, computation of complex roots should not result in a "nan" and "-nan" output and it should be solved and printed in "x + yi" and "x-yi" format (x is the real part and yi is the imaginary part).

The whole program should be able to run as many times the user wants.

Sample output format (You do not have to follow the structure given here but the required information should be present):
Your quadratic equation, 2x^2 + 4x + 2 has two real equal roots.
The value of the roots are,
root1 = -1
root2 = -1

Inputs to test (a, b, c):
1. (0 , 5 ,2)
2. (4, 7 ,3)
3. (2, 9, 11)
4. (3, 6, 3)

Answer 1

#include <iostream>
#include <string>
#include <cmath>

using namespace std;

//Function declaration
int getInput(char coeff);
int validate(int &n);
pair<double, double> solve(int a, int b , int c);
void display(int a, int b , int c, double root1, double root2);

//Gets the user input for the coefficients
int getInput(char coeff)
{
int n = 0;
do
{
cout << "Enter the value of " << coeff << ": ";
cin >> n;
} while(validate(n));
}

//Checks if the value of n is zero
int validate(int &n)
{
if(n == 0)
{
cout << "The value cannot be zero. Please try again" << endl;
return 1;
}
return 0;
}

//Solves the equation and returns the root(s)
pair<double, double> solve(int a, int b , int c)
{
double root1 = 0, root2 = 0;
  
//Calculations
int discriminant = pow(b, 2) - (4 * a * c);
if(discriminant < 0)
{
root1 = NAN;
root2 = -NAN;
}
else if(discriminant == 0)
{
root1 = ((-1) * b) / (2 * a);
root2 = root1;
}
else
{
root1 = (((-1) * b) + sqrt(discriminant)) / (2 * a);
root2 = (((-1) * b) - sqrt(discriminant)) / (2 * a);
}
  
return make_pair(root1, root2);
}

//Displays the result
void display(int a, int b , int c, double root1, double root2)
{
cout << endl;
cout << "Your quadratic equation, " << a << "x^2 ";
if(b < 0)
cout << "- " << b;
else
cout << "+ " << b;
  
if(c < 0)
cout << "x - " << c << " has ";
else
cout << "x + " << c << " has ";
  
//Chek if roots are real or complex
if(root1 == -1)
cout << "two distinct complex roots.";
else if(root1 == root2)
cout << "two equal real roots.";
else if(root1 != root2)
cout << "two distinct real roots.";
  
//Display roots
cout << endl << "The value of the roots are, " << endl;
cout << "root1 = " << root1 << endl;
cout << "root2 = " << root2 << endl << endl;
}

int main()
{
char ch = 'y';
  
while((ch == 'y') || (ch == 'Y')) {
int a, b, c;
  
//Accept values of a, b, c from user
a = getInput('a');
b = getInput('b');
c = getInput('c');
  
//Solve Equation
pair<double, double> roots = solve(a, b, c);
  
//Display results
display(a, b, c, roots.first, roots.second);
  
//Ask if the user wants to continue
cout << "Do you want to continue [y/n]: ";
cin >> ch;
  
cout << endl;
}
}

SAMPLE OUTPUT:

Enter the value of a: 0 The value cannot be zero. Please try again Enter the value of a:4 Enter the value of b: 7 Enter the value of c 3 Your quadratic equation, 4x*2 7x 3 has two distinct real roots. The value of the roots are, rooti0.75 root2-1 Do you want to continue [y/n]: y Enter the value of a: 2 Enter the value of b:9 Enter the value of c: 11 Your quadratic equation, 2x29x 11 has two distinct real roots. The value of the roots are, rootlnan Do you want to continue [y/n]: y Enter the value of a: 3 Enter the value of b: 6 Enter the value of c:3 Your quadratic equation, 3x*2 + 6x3 has two distinct complex roots. The value of the roots are, root2--1 Do you want to continue [y/n]:n