By Gary Jones
on March 21, 2004

Version: 1.0

Type: Function

Category: Math Functions

Description: A PHP function that uses the syntax such as quadratic(3, 4, 5, ‘both’) to return both roots of the quadratic formula 3x^2+4x+5=0.

Originally written as a javascript function, it’s been converted to PHP, but has been tested to give real roots, repeated roots, and will even give complex roots. Each section is commented, but you will obviously need to know and understand how to solve quadratic equations to understand the maths behind the PHP!

As always, feel free to tweak it for your own use, or submit a new version if you find a bug!

Enjoy, Gazza.

```// Quadratic Solver for PHP by Gazza 2004-03-21
// Useage: for 3x^2 + 4x + 5 = 0, use quadratic(3, 4, 5, 'root1') and quadratic(3, 4, 5, 'root2'),
// or simply just quadratic(3, 4, 5, 'both').
// The \$root argument doesn't define which value it will be in relation to the other - I could
// easily have called them John and Jane, instead of 1st and 2nd.
//
{
\$precision = 3; // Change this value for a different decimal places rounding.

\$bsmfac = \$b*\$b-4*\$a*\$c;
if (\$bsmfac < 0) { // Accounts for complex roots.
\$plusminusone = " + "; \$plusminustwo = " - ";
\$bsmfac *=-1;
\$complex=(sqrt(\$bsmfac)/(2*\$a));
if (\$a < 0){ //if negative imaginary term, tidies appearance.
\$plusminustwo = " + ";
\$plusminusone = " - ";
\$complex *= -1;
} // End if (\$a < 0)
\$lambdaone = round(-\$b/(2*\$a), \$precision).\$plusminusone.round(\$complex, \$precision).'i';
\$lambdatwo = round(-\$b/(2*\$a), \$precision).\$plusminustwo.round(\$complex, \$precision).'i';
} // End if (\$bsmfac < 0)

else if (\$bsmfac == 0) { // Simplifies if b^2 = 4ac (real roots).
\$lambdaone = round(-\$b/(2*\$a), \$precision);
\$lambdatwo = round(-\$b/(2*\$a), \$precision);
} // End else if (bsmfac == 0)

else { // Finds real roots when b^2 != 4ac.
\$lambdaone = (-\$b+sqrt(\$bsmfac))/(2*\$a);
\$lambdaone = round(\$lambdaone, \$precision);
\$lambdatwo = (-\$b-sqrt(\$bsmfac))/(2*\$a);
\$lambdatwo = round(\$lambdatwo, \$precision);
} // End else

// Return what is asked for.
if (\$root == 'root1') {return \$lambdaone;}
if (\$root == 'root2') {return \$lambdatwo;}
if (\$root == 'both') {return \$lambdaone. ' and ' .\$lambdatwo;}
} // End function```
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