// Roots of a quadratic equation a*x**2 +b*x +c = 0
// Reads a,b,c and computes the roots using the quadratic formula
// Michael Rothstein
// 01/29/2014

#include <iostream>
#include <cmath>

using std::cin; using std::cout; using std::endl;

int main(){
  // Input the data
  cout << "Enter the coefficients of the quadratic equation: ";
  double a,b,c;
  cin >> a >> b >> c;

  if ( a == 0 ) { // linear equation or nonsense
    if ( b == 0 ) { // nonsense equation
      cout << "a is 0 and b is 0; this is not a real equation.\n";
      return 0;
    }

    else { // linear equation b*x + c = 0
      cout << "a is 0 and the root of the equation " << b << "*x + " << c 
           << " = 0 is " << -c/b << endl;
      return 0;
    }
  }

  else { // Real quadratic equation
    double discriminant = b*b - 4*a*c;
    cout << "The equation " << a << "*x**2 + " << b << "*x + " << c << " = 0 ";

    if ( discriminant == 0 ){ // two equal roots
      cout << "has two equal roots which are :" << -b/(2*a) << endl;
      return 0;
    }

    else if ( discriminant > 0 ) { // two real roots
      double d1 = sqrt(discriminant);
      double root1 = (-b+d1)/(2*a);
      double root2 = (-b-d1)/(2*a);
      cout << "has two real roots which are: " << root1 << " and " 
	   << root2 << endl;
      return 0;
    }

    else { // two complex roots
      double imag_part = sqrt(-discriminant)/(2*a);
      double real_part = (b==0?0:-b/(2*a));
      cout << "has two complex roots: " << real_part << " +/- " 
	   << imag_part << "*I\n";
      return 0;
    }
  }
}