20_quadratic_roots.cpp

//Calculate the roots of a quadratic equation using the discriminant.
#include <iostream>
#include <cmath>
using namespace std;

int main()
{
    //ax^2+bx+c=0 is the quadratic equation
    //b^2-4ac is discriminant.

    double D,a,b,c;
    //let D be Discriminant.

    cout<< "Enter the value of 'a': "; //asking user for the input
    cin>>a;                            //initializing it with user input

    cout<< "Enter the value of 'b': "; //asking user for the input
    cin>>b;                            //initializing it with user input

    cout<< "Enter the value of 'c': "; //asking user for the input
    cin>>c;                            //initializing it with user input

    if (a == 0) 
    {
        if (b == 0) //if a=0, and also b=0, do...
        {
            if (c == 0) //if all three a = b = c = 0, do...
            {
                cout<< "Infinite solutions (Identity equation)" <<endl; //print this
            }
            else    // if c!=0 then print the following
            {
                cout<< "No Solution (Contadiction)"<<endl;
            }
        }
        else   //if b!=0 do the following
        {
            double x = -c/b ;  //formula.
            cout << "(Linear Equation) One root at 'x' = "<< x <<endl; //printing the result
        }
    }
    else //if a != 0 , do the following
    {
        D= (b*b)- 4*a*c ; //formula
        cout<< "Discriminant is: "<< D<< endl; //print the value of discriminant

        
        if ( b == 0) //when b =0 
        {
            if (c == 0) //when b and c both = 0
            {
                cout<<"No solution (Contradiction)"<<endl; //print this.
            }
            else //when c!= 0
            {
                double x = -c/a;   //formula
                cout<< "(Linear Equation) One root at x = "<<x<<endl; //print this.
            }
        }
        else if (c == 0) //when c=0
            {
                cout<<"x = 0 "<<endl; //print this and also
                cout << "Another root at x = " << (-b / a) << endl;// print this
            }
        
        else if (D > 0) //when discriminant is greater than zero then...
        {
            double x1 = (-b + sqrt(D)) / (2 * a); //formula
            double x2 = (-b - sqrt(D)) / (2 * a); //formula
            cout << "Distinct Real Roots: Root 1 = " << x1 << ", Root 2 = " << x2 << endl; //print the roots of the equation
        }
        else if (D == 0) //when discriminant is = 0 , then...
        {
            double x = -b / (2 * a); //formula
            cout << "Repeated Real Root: x = " << x << endl; //print the root
        }
        else //when dicriminant is lesser than zero ,then...
        {
            double real = -b / (2 * a); //formula
            double imaginary = sqrt(abs(D)) / (2 * a); //formula
            cout << "Complex Roots: Root 1 = " << real << " + " << imaginary << "i, Root 2 = " << real << " - " << imaginary << "i" << endl; //print the roots of the equation
        }
    }

    return 0; //end of this
}