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A simple program to solve quadratic equations with

By , 10 Nov 2010
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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, see
numerical recipes in C and the Wolfram site at
#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; }
   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; }
   if ( fabs(b)>1.0e-16 )  { bsign=b/fabs(b); }
   else { if ( b<0.0e+00 ) { bsign=-1.0e+00; } }
   // 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;
      x1=y1; x2=y2;
   return true;


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

About the Author

Software Developer (Senior)
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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 7:17 
GeneralOh well, thanks Alain, I didn't know the standard evoluted t... Pinmemberfederico.strati9-Nov-10 23:07 
General#include &lt;limits&gt; const double eps = std::numeric_limi... PinmemberAlain Rist9-Nov-10 22:34 
GeneralOh well, the machine epsilon is around 3x10-8 for single pre... Pinmemberfederico.strati9-Nov-10 4:38 
GeneralReason for my vote of 2 Aren't the tolerance values arbitrar... PinmemberYvesDaoust8-Nov-10 23:30 
GeneralThe inputs "y" and "z" serve the only purpose of finding a r... Pinmemberfederico.strati8-Nov-10 22:23 
GeneralCan you elaborate on the function of the 2 added inputs y an... Pinmemberbstrack8-Nov-10 21:27 
Can you elaborate on the function of the 2 added inputs y and z? That is, why are they needed since only the order of the roots is affected? Why not just use x1=q/a and x2=c/q?

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