//racines de polynomes du second degré 
//eqn:  ax^2 + bx + c = 0
//racines: x = (-b +/-sqrt(b^2 - 4ac))/2a   
#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

int main() {
  double a, b, c;
  cout << "Quels sont les coefficients de l'equation ?" << endl;
  cin >> a >> b >>c;
  
  double x1, x2;
  double delta;  
  if (a!=0.) { 
    delta = b*b - 4*a*c;
    if (delta<0.)
      cout << "Il n'y a pas des solutions reelles !" << endl;
    else if (delta == 0.) {
      x1 = x2 = -b/(2.*a);
      cout << "Il y a deux solutions identiques : " << x1 << endl;
    }
    else {     //delta > 0.
      x1 = (-b + sqrt(delta)) / (2.*a);
      x2 = (-b - sqrt(delta)) / (2.*a);
      cout << "Les solutions sont : x1 = "  << setprecision(20) << x1
                              << ", x2 = "  << setprecision(20) << x2 << endl; 
    } 
  }   
  else
    cout << "a est nul, pas de solutions !" << endl;
  
  //verification
  if(delta>=0. && a!=0.) {
    double y1, y2;
    y1 = a*x1*x1 + b*x1 + c;
    y2 = a*x2*x2 + b*x2 + c;
    cout << "Verification x1 : "  << setprecision(20) << y1 << endl;
    cout << "Verification x2 : "  << setprecision(20) << y2 << endl;
  }

  return 0;
}