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A simple program to solve quadratic equations with

, 10 Nov 2010 CPOL
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The correct way to solve quadratic equations is none of the above. For the correct algorithm as applied in the following function, seenumerical recipes in C and the Wolfram site at http://mathworld.wolfram.com/QuadraticEquation.html#include bool quadratic(double a, double b,...
The correct way to solve quadratic equations is none of the above. For the correct algorithm as applied in the following function, see
numerical recipes in C and the Wolfram site at http://mathworld.wolfram.com/QuadraticEquation.html
 
#include <limits>
bool quadratic(double a, double b, double c, double& x1, double& x2, double y, double z)
{
   double delta=0.0e+00, q=0.0e+00, bsign, y1, y2;
   const double eps = std::numeric_limits()<double>.epsilon();
   // equation is: a*x^2 + b*x + c = 0; a cannot be zero.
   if ( fabs(a) <= eps ) { return false; }
 
   delta=b*b-4.0*a*c;
   if ( delta<0.0e+00 ) { return false; }
   if ( delta>=0.0e+00 && delta <= eps )
   { x1=(-1.0*b/(2.0*a)); x2=x1; return true; }
 
   bsign=1.0e+00;
   if ( fabs(b)>1.0e-16 )  { bsign=b/fabs(b); }
   else { if ( b<0.0e+00 ) { bsign=-1.0e+00; } }
 
   q=(-0.5)*(b+bsign*sqrt(delta));
 
   // the roots of the equation are:
   y1=q/a; y2=c/q;
 
   // find if any of the roots is in the given [y,z] interval
   if (( y<=y1 )&&( y1<=z ))
   {
      x1=y1; x2=y2;
   }
   else if (( y<=y2 )&&( y2<=z ))
   {
      x1=y2; x2=y1;
   }
   else
   {
      x1=y1; x2=y2;
   }
 
   return true;
}

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

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About the Author

federico.strati
Software Developer (Senior)
Italy Italy
Senior Software Developer in C/C++ and Oracle.
Ex-physicist holding a Ph.D. on x-ray lasers.

Comments and Discussions

 
GeneralI edited my answser to address your objection. evviva :) PinmemberAlain Rist16-Nov-10 8:17 
GeneralOh well, thanks Alain, I didn't know the standard evoluted t... Pinmemberfederico.strati10-Nov-10 0:07 
General#include &lt;limits&gt; const double eps = std::numeric_limi... PinmemberAlain Rist9-Nov-10 23:34 
#include <limits> const double eps = std::numeric_limits<double>::epsilon(); Smile | :)
GeneralOh well, the machine epsilon is around 3x10-8 for single pre... Pinmemberfederico.strati9-Nov-10 5:38 
GeneralReason for my vote of 2 Aren't the tolerance values arbitrar... PinmemberYvesDaoust9-Nov-10 0:30 
GeneralThe inputs "y" and "z" serve the only purpose of finding a r... Pinmemberfederico.strati8-Nov-10 23:23 
GeneralCan you elaborate on the function of the 2 added inputs y an... Pinmemberbstrack8-Nov-10 22:27 

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