13,197,200 members (57,682 online)
Alternative Tip/Trick
alternative version

Stats

10K views
2 bookmarked
Posted 5 Nov 2010

A simple program to solve quadratic equations with

, 10 Nov 2010
 Rate this:
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;
}```

Share

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

 First Prev Next
 I edited my answser to address your objection. evviva :) Alain Rist16-Nov-10 7:17 Alain Rist 16-Nov-10 7:17
 Oh well, thanks Alain, I didn't know the standard evoluted t... federico.strati9-Nov-10 23:07 federico.strati 9-Nov-10 23:07
 #include <limits> const double eps = std::numeric_limi... Alain Rist9-Nov-10 22:34 Alain Rist 9-Nov-10 22:34
 Oh well, the machine epsilon is around 3x10-8 for single pre... federico.strati9-Nov-10 4:38 federico.strati 9-Nov-10 4:38
 Reason for my vote of 2 Aren't the tolerance values arbitrar... YvesDaoust8-Nov-10 23:30 YvesDaoust 8-Nov-10 23:30
 The inputs "y" and "z" serve the only purpose of finding a r... federico.strati8-Nov-10 22:23 federico.strati 8-Nov-10 22:23
 Can you elaborate on the function of the 2 added inputs y an... bstrack8-Nov-10 21:27 bstrack 8-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?
 Last Visit: 31-Dec-99 18:00     Last Update: 20-Oct-17 12:44 Refresh 1