Numerical Quadratic Equation Solver

[JayT]

Here is a function I threatened to post earlier.
It works in PHP 4 and 5.

It simply computes the numerical solutions,
real and imaginary, for a standard quadratic
equation of the general form

Ax² + Bx + C = 0





USAGE EXAMPLES

To find the real roots of the quadratic equation:

2x² + *4x - *56 = 0

print Quad_Solve("2", "*4", "-*56");

/*

Returned result

x* = -**
x2 = 6

*/

To find the complex (imaginary) roots of the quadratic equation:

*6x² - *0x + 4 = 0

print Quad_Solve("*6", "-*0", "4");

/*

Returned result

x = 0.**25 ± 0.**0**2*748**8**88786 i

The (i) at the end indicates a complex (imaginary) root.

*/

Here is the PHP code for the function:

/*

   This function solves a quadratic
   equation of the general form

   Ax² + Bx + C = 0

   for numerical roots x* and x2

   The solutions may be real or complex (imaginary).

   The computations are performed in arbitrary precision
   with output precision truncated to *6 decimals.

*/



   function Quad_Solve($Aarg, $Barg, $Carg)

{

// ---------------------
// Read A,B,C arguments.

   $A = trim($Aarg);
   $B = trim($Barg);
   $C = trim($Carg);

// --------------------------------
// Set internal decimals precision.

   $DP = 20;

// ------------------------------------------
// Compute discriminant D.  If negative, then
// the solutions are complex (imaginary).

   $w* = bcMul($B, $B, $DP); // B²

   $w2 = bcMul("4", bcMul($A, $C, $DP), $DP); // 4AC

    $D = bcSub($w*, $w2, $DP);

// -----------------------------------------------
// Determine if quadratic root is real or complex.

   $i = "";

   if (bcComp($D, "0", $DP) < 0)

      {
       $i = "<B> i</B>";  $D = bcSub("0", $D, $DP);
      }

//  --------------------------
//  Compute values of u and v.

    $u = bcDiv(bcSub("0", $B, $DP), bcMul("2", $A, $DP), $DP); // -B/2A

   $w* = bcSqRt($D, $DP); // SqRt(B² - 4AC) = SqRt(D)

    $v = bcDiv($w*, bcMul("2", $A, $DP), $DP); // SqRt(B² - 4AC) / 2A

// -----------------------------
// Do this if roots are complex.

   if ($i != "")
      {
       $u = RTrim(RTrim($u, "0"), ".");
       $v = RTrim(RTrim($v, "0"), ".");
       return "<PRE>x = $u &plusmn; $v$i</PRE>";
      }

// --------------------------
// Do this if roots are real.

   $x* = RTrim(RTrim(bcSub($u, $v, *6), "0"), ".");
   $x2 = RTrim(RTrim(bcAdd($u, $v, *6), "0"), ".");
   return "<PRE>x* = $x*\nx2 = $x2</PRE>";


} // End of  Quad_Solve()

Hope someone finds this useful.

Cheers!

[Moonbat]

A few years ago, this would've helped me pwn my homework, but this still is useful (but not nearly as useful as it would've been had I met you before this time). Thanks a load for this

P.S. - Can you make a program that can factor polynomials (anywhere from binomials to hexanomials) please?

[JayT]

A few years ago, this would've helped me pwn my homework, but this still is useful (but not nearly as useful as it would've been had I met you before this time). Thanks a load for this

P.S. - Can you make a program that can factor polynomials (anywhere from binomials to hexanomials) please?

Factoring is a complicated process.
The three main reasons are because trial an error is involved in some cases, in some other cases factoring is impossible and in other cases, some factors can be mixed (real and complex).

I'll have to study that problem more, but it's a good idea.

I crossed swords with that problem quite a few times. It left some scars.

[Ezekiel]

I'm wondering, do you have anything on your site (or code snippets) relating to surds?

I'm too lazy to do another one of these:

[url]http://www.divshare.com/image/208727*-eab[/url]

Edit: I got five tails on my first try of your random coin flipper! What are the chances of that? I guess I've won the internet now.

[JayT]

I'm wondering, do you have anything on your site (or code snippets) relating to surds?

I'm too lazy to do another one of these:

[url]http://www.divshare.com/image/208727*-eab[/url]

Edit: I got five tails on my first try of your random coin flipper! What are the chances of that? I guess I've won the internet now.

Yes! You've won the Internet! Take it home with you!
LOL


The chances of 5 tails in a row is identical to the chances of 5 heads in a row.

Actually */*2

* : (Possible outcomes per trial) ^ Trials = *:(2 ^ 5) = *:*2


Odds of tossing n heads (or tails) in a row = *:(2 ^ n)

Odds of getting *0 true/false questions *00&#*7; wrong/correct by random guessing alone:

*:(2 ^ *0) = *:*024

etc.


The things on that site are basically my PHP learning experiments.





**************

If you mean the essential rules of working with surds, I don't have too much at this time. Still updating some things in the background.


That math sheet image brings back some memories.
LOL

I do have lots of math notes that I'm slowly converting into PHP web pages, like I did with the quadratic function. Some are on the subject of surds, but not yet made into web pages.

One reason it takes me so long is because I'm fanatically fussy about quality. I test a page to death to make sure it works correctly.

I didn't exactly expect many would be too interested, so I wasn't in a rush. Math usually scares people.

:)

Math is much easier to learn when there is a real-world physical problem to which to apply it and see what the numbers are for and where they come from and how they relate to the problem.

That's my focus - practical math. They spend too much time on theory before the student has had a chance to relate it to reality. Much harder to learn it that way. Schools are in such a mad rush these days.

When is the last time you encountered a problem in the real world (other than a school exam) that you would tackle by using a quadratic equation? Would you recognise such a problem if it was in front of you? Schools seem to miss this point.








At the moment, one of my web hosts is slowing me down. I was supposed to be moved to a different server back on the 2*st so both of my sites would be using PHP5, but it hasn't happened yet, so I can't get much done until they do it.


Time to send them an email and inquire about the problem.

[Ezekiel]

Yes! You've won the Internet! Take it home with you!
LOL


The chances of 5 tails in a row is identical to the chances of 5 heads in a row.

Actually */*2

* : (Possible outcomes per trial) ^ Trials = *2 ^ 5) = *:*2


Odds of tossing n heads (or tails) in a row = *2 ^ n)

Odds of getting *0 true/false questions *00&#*7; wrong/correct by random guessing alone:

*2 ^ *0) = *:*024

Yeah I'm pretty good with probability, but it's nice to have someone do the work for you .

So they're all exponents of two. Makes sense.

I still think */*2 is an impressive gamble to win at. Yesterday must have been my lucky day.

Aw crap, what does that mean for today then?

If you mean the essential rules of working with surds, I don't have too much at this time. Still updating some things in the background.

Oh god, this means I'll have to do homework. You can not underestimate the seriousness of this situation.

That math sheet image brings back some memories.

Good or bad?

Math is much easier to learn when there is a real-world physical problem to which to apply it and see what the numbers are for and where they come from and how they relate to the problem.

That's my focus - practical math. They spend too much time on theory before the student has had a chance to relate it to reality. Much harder to learn it that way. Schools are in such a mad rush these days.

When is the last time you encountered a problem in the real world (other than a school exam) that you would tackle by using a quadratic equation? Would you recognise such a problem if it was in front of you? Schools seem to miss this point.

No, I certainly can not think of any real-life application of these things; especially surds.

That is of course unless I plan to live a highly-scientific life and become a world-renowned rocket-scientist, but that's not really how I roll [read: too lazy].

At the moment, one of my web hosts is slowing me down. I was supposed to be moved to a different server back on the 2*st so both of my sites would be using PHP5, but it hasn't happened yet, so I can't get much done until they do it.

[url]www.nearlyfreespeech.net[/url]

Pay for what you use. I have so far paid about $*0 to keep my site running for many months. That's with MySQL, mail-forwarding -- the whole deal.

Give them a try.