Exercise 3.1: polynomial-2.0.cpp

//polynomial-2.0.cpp
//Simple program to solve polynomial equations up to 2nd order.
//Adapts polynomial-1.0.cpp to give better output when
//coefficients a and b are zero.
//Reads coefficients from keyboard and outputs to screen.
//Uses complex numbers for quadratic solutions.
//Steven Bamford

#include <cstdlib>
#include <iostream>
#include <cmath>
#include <complex>
using namespace std;

int main()
{
  double a, b, c;  //coefficients of polynomial
                   //a*x*x + b*x + c = 0
  const double epsilon = 1.0e-300; //a few magnitudes
             //larger than the smallest double number

  cout << "Enter coefficients a, b, and c:" << endl;
  cin >> a >> b >> c;  //read coeffs from keyboard
  
  if (abs(a) < epsilon)  //if a is zero
    { 
      if (abs(b) < epsilon)
	{//no solution
	  cout << "There is no solution for a = b = 0!" << endl
	       << "a and/or b must be non-zero for a solution" << endl;
	}
      else
	{//linear
	  double xr;   // one real solution
	  xr = -c/b;
	  cout << "Solution is: " << xr << endl;
	}
    }
  else //if a is non-zero
    { //quadratic
      complex<double> des;      //variable for the discriminant
      complex<double> x1, x2;   //two complex solutions
      des = b*b - 4*a*c;            //calc discriminant
      x1 = (-b + sqrt(des))/(2*a);  //solution 1
      x2 = (-b - sqrt(des))/(2*a);  //solution 2
      cout << "Solutions are: " << x1 << " and " << x2 << endl;
    }

  system("PAUSE");
  return(0);
}