// Demo program for CS 149. v. Nov. 10, 2000

//  Find roots of quadratic equation.  If b^2 -4ac is
//  approximately zero, then the solutions printed with
//    the standard formuation of the quadratic formula may
//    not be accurate.  However with reformulation, the
//    problem may be avoided.

// Input:  Three real coefficients of a quadratic equation:
//   in the order a, b, c for the equation
//                 a*x^2 + b*x + c = 0.
//   Prompts for input and repeats until EOF.

// Output:  Roots of the polynomial.

// Assumptions:  Three numberic inputs will be provided.

#include <iostream.h>
#include <math.h>
#include <stdlib.h>

int main()
{
	// Functions to compute real roots of quadratic equation.
	double Root1Eq1( double a, double b, double c );
	double Root2Eq1( double a, double b, double c );
	double Root1Eq2( double a, double b, double c );
	double Root2Eq2( double a, double b, double c );
	double CompDisc( double a, double b, double c );
	void CheckReport( double a, double b, double c, double root1, double root2 );
	double CheckAns( double a, double b, double c, double ans );

	double x1,    // First real root of equation	
      x2,	   // Second real root of equation
      a,       // Coefficient of x^2
      b,       // Coefficient of x
      c,       // Constant term
      Disc;    // Discriminant:  sqrt(b^2 - 4ac)

     while( !cin.eof() )
	 {
		// Read, echo and check input. }
			cout << "Enter coefficients of quadratric equation a, b, and c:" << endl;
			cin >> a >> b >> c;
			cout << "Finding roots of equation:" << endl;
			cout << "  " << a << " x^2 + " << b << " x + " << c << " = 0" << endl;

		Disc = CompDisc( a, b, c );
		// Standard formulation of quadratic formula
			x1 = Root1Eq1( a, b, c );
			x2 = Root2Eq1( a, b, c );
		CheckReport( a, b, c, x1, x2 );
		// Alternate formulation of quadratic formula
			x1 = Root1Eq2( a, b, c );
			x2 = Root2Eq2( a, b, c );
		CheckReport( a, b, c, x1, x2 );
		// Try branching on sign of b
		cout << "Roots computed based on sign of b" << endl;
		if ( b > 0 )
		{
			x1 = Root1Eq2( a, b, c );
			x2 = Root2Eq1( a, b, c );
		}
		else
		{
			x1 = Root1Eq1( a, b, c );
			x2 = Root2Eq2( a, b, c );

		} // else
		CheckReport( a, b, c, x1, x2 );
	} // while !eof

     return 0;

} // main

// Function definitions
// Disc computes the discriminant if it is real.
double CompDisc( double a, double b, double c )
{
	double ans;

	ans = b*b -4.0*a*c;
	if ( ans < 0.0 )
	{
		cout << "Error in function Disc: imaginary roots" << endl;
		exit( EXIT_FAILURE );
	}
	else
		return sqrt( ans );
}

// Compute one real root using standard formula
// a, b, and c are coefficients of quadratic.
// This function assumes real, not imaginary, roots
double Root1Eq1( double a, double b, double c )
{
	double CompDisc( double a, double b, double c );

	return (-b + CompDisc(a,b,c))/ ( 2.0 * a );
}

// Compute second real root using standard formula
// a, b, and c are coefficients of quadratic.
// This function assumes real, not imaginary, roots
double Root2Eq1( double a, double b, double c )
{
	double CompDisc( double a, double b, double c );

	return (-b - CompDisc(a,b,c))/ ( 2.0 * a );
}

// Compute one real root using alternate formula
// a, b, and c are coefficients of quadratic.
// This function assumes real, not imaginary, roots
double Root1Eq2( double a, double b, double c )
{
	double CompDisc( double a, double b, double c );

	return ( 2.0 * c ) / ( -b - CompDisc(a,b,c) );
}

// Compute second real root using alternate formula
// a, b, and c are coefficients of quadratic.
// This function assumes real, not imaginary, roots
double Root2Eq2( double a, double b, double c )
{
	double CompDisc( double a, double b, double c );

	return ( 2.0 * c ) / ( -b + CompDisc(a,b,c) );
}

// Check answer.
// a, b, and c are coefficients of quadratic, x is value to be checked.
double CheckAns( double a, double b, double c, double x )
{
	return a*x*x + b*x + c;
}

// Check Report.
// a, b, and c are coefficients of quadratic, x is value to be checked.
void CheckReport( double a, double b, double c, double x1, double x2 )
{
	cout << "Roots using alternate formulation" << endl;
	cout << "  First root:   " << x1 << endl;
	cout << "  Second root:  " << x2 << endl;
	cout << "Checking answer: " << endl;
	cout << "  First root:  ax^2 + bx + c = " <<
		CheckAns( a, b, c, x1 ) << endl;
	cout << "  Second root:  ax^2 + bx + c = " <<
		CheckAns( a, b, c, x2 ) << endl;

}