/* Program to run the quadratic formula through */


#include<math.h>
#include<iostream>
using namespace std;

void standard_quadratic(double a, double b, double c, double *root1, double *root2)
{
  *root1=-(b+sqrt(b*b-4.0*a*c))/(2.0*a);
  *root2=-(b-sqrt(b*b-4.0*a*c))/(2.0*a);
  return;
}

double parabola(double a,double b,double c,double x)
{
  double y;
  y=a*x*x+b*x+c;
  return y;
}

void viete_formula(double a, double b, double c, double *root1, double *root2)
{
  /* We have two relations: x_1+x_2 = -b/a, and x_1*x_2=c/a */ 
  /* Let's find the first good root */
  if (b>=0) 
    {
      *root1=-(b+sqrt(b*b-4.0*a*c))/(2.0*a);
      *root2=c/(a*(*root1));
    }
  else
    {
      *root1=-(b-sqrt(b*b-4.0*a*c))/(2.0*a);
      *root2=c/(a*(*root1));      
    }
  return;
  }

main()
{
  double a,b,c,y;
  double root1,root2;
  cout << "Enter a,b,c for the parabola.\n";
  cin >> a >> b >> c;
  cout << "a,b,c" << a<<" "<< b << " "<< c << " " << endl;
  standard_quadratic(a,b,c,&root1,&root2);
  cout << "For the standard quadratic, the roots are: " << root1 << " " << root2 << endl;
  cout << "For the roots times 10^5 are:" << 1.0e5*root1 << " " << 1.0e5*root2 << endl;
  y=parabola(a,b,c,root1);
  cout << "Putting first value back in gives " << y << endl;
  y=parabola(a,b,c,root2);
  cout <<"Putting second value back in gives " << y << endl;
  viete_formula(a,b,c,&root1,&root2);
  cout <<"For the standard quadratic, the roots are: "<< root1 << " " << root2 << endl;
  cout << "For the roots times 10^5 are: " << (1.0e5*root1) << " " << 1.0e5*root2 << endl;
  y=parabola(a,b,c,root1);
  cout << "Putting first value back in gives " << y << endl;
  y=parabola(a,b,c,root2);
  cout <<"Putting second value back in gives " << y << endl;


}