General
This script can solve quartic equations in the form of ax^4 + bx+3 + cx^2 + dx + e = 0.
Notes
- Created by: Brian Kieffer
- Web Site: http://www.freewebs.com/brianjs/
Source Code
Paste this source code into the designated areas.
External file
Paste this code into an external JavaScript file named: quarticSolver.js
/* This script and many more are available free online at
The JavaScript Source!! http://javascriptsource.com
Created by: Brian Kieffer | http://www.freewebs.com/brianjs/ */
function calcmult(a2,b2,c2,d2,e2) {
var real = a2*c2 – b2*d2
var img = b2*c2 + a2*d2
if (e2 == 0) {
return real
} else {
return img
}
}
function isquareroot(a1,b1,n1) {
var y = Math.sqrt((a1*a1) + (b1*b1));
var y1 = Math.sqrt((y – a1) / 2);
var x1 = b1 / (2*y1);
if (n1 == 0) {
return x1
} else {
return y1
}
}
function extractcoefficents() {
// Extract X^4 Coefficent
var aq = document.numbers2.a.value;
var aq2 = aq // Keeps Orignial AQ value
// Extract X^3 Coefficent
var bq = document.numbers2.b.value;
var bq2 = bq // Keeps Orignial BQ Value
// Extract X^2 Coefficent
var cq = document.numbers2.c.value;
// Extract X Coefficent
var dq = document.numbers2.d.value;
// Extract Constant
var eq = document.numbers2.e.value;
// Define Perfect Quartic Varible
var perfect = 0;
var perfectbiquadratic = 0;
// The Bi-Quadratic 2 Perfect Squares that are negative test
if (cq*cq – 4*aq*eq == 0 && cq > 0) {
perfectbiquadratic = 1;
}
// Divide Equation by the X^4 Coefficent to make equation in the form of X^4 + AX^3 + BX^2 + CX + D
bq /= aq;
cq /= aq;
dq /= aq;
eq /= aq;
aq = 1;
var f2 = cq – (3*bq*bq / 8);
var g2 = dq + (bq*bq*bq/8) – (bq*cq/2);
var h2 = eq – (3*bq*bq*bq*bq/256) + (bq*bq*(cq/16)) – (bq*dq/4);
var a = 1;
var b = f2/2
var c = (f2*f2 – (4*h2)) / 16
var d = -1*((g2*g2)/64)
if (b == 0 && c == 0 && d == 0) {
perfect = 1
}
// Cubic routine starts here…..
var f = (((3*c) / a) – ((b*b) / (a*a))) / 3;
var g = (((2*b*b*b) / (a*a*a)) – ((9*b*c) / (a*a)) + ((27*d) / a)) / 27
var h = eval(((g*g)/4) + ((f*f*f)/27))
var z = 1/3;
var i;
var j;
var k;
var l;
var m;
var n;
var p;
var xoneterm;
var xtwoterm;
var xthreeterm;
var alreadydone;
var alreadydone2 = 0;
var ipart = 0;
var p = 0
var q = 0
var r = 0
var s = 0
if (h <= 0) {
var exec = 2
i = Math.sqrt(((g*g) / 4) – h);
j = Math.pow(i,z);
k = Math.acos(-1 * (g / (2*i)));
l = -1*j;
m = Math.cos(k / 3);
n = Math.sqrt(3) * Math.sin(k / 3);
p = (b / (3*a)) * -1;
xoneterm = (2*j) * Math.cos(k/3) – (b / (3*a));
xtwoterm = l * (m + n) + p;
xthreeterm = l * (m – n) + p;
}
if (h > 0) {
var exec = 1
var R = (-1*(g / 2)) + Math.sqrt(h);
if (R < 0) {
var S = -1*(Math.pow((-1*R),z))
} else {
var S = Math.pow(R,z);
}
var T = (-1*(g / 2)) – Math.sqrt(h);
if (T < 0) {
var U = -1*(Math.pow((-1*T),z));
} else {
var U = Math.pow(T,z);
}
xoneterm = (S + U) – (b / (3*a));
xtwoterm = (-1*(S+U)/2) – (b / (3*a));
var ipart = ((S-U) * Math.sqrt(3)) / 2;
xthreeterm = xtwoterm;
}
if (f == 0 && g == 0 && h == 0) {
if ((d/a) < 0 ) {
xoneterm = (Math.pow((-1*(d/a)),z));
xtwoterm = xoneterm;
xthreeterm = xoneterm;
} else {
xoneterm = -1*(Math.pow((d/a),z));
xtwoterm = xoneterm;
xthreeterm = xoneterm;
}
}
// ….and ends here.
// Return to solving the Quartic.
if (ipart == 0 && xoneterm.toFixed(10) == 0) {
var alreadydone2 = 1
var p2 = Math.sqrt(xtwoterm)
var q = Math.sqrt(xthreeterm)
var r = -g2 / (8*p2*q)
var s = bq2/(4*aq2)
}
if (ipart == 0 && xtwoterm.toFixed(10) == 0 && alreadydone2 == 0 && alreadydone2 != 1) {
var alreadydone2 = 2
var p2 = Math.sqrt(xoneterm)
var q = Math.sqrt(xthreeterm)
var r = -g2 / (8*p2*q)
var s = bq2/(4*aq2)
}
if (ipart == 0 && xthreeterm.toFixed(10) == 0 && alreadydone2 == 0 && alreadydone2 != 1 && alreadydone2 != 2) {
var alreadydone2 = 3
var p2 = Math.sqrt(xoneterm)
var q = Math.sqrt(xtwoterm)
var r = -g2 / (8*p2*q)
var s = bq2/(4*aq2)
}
if (alreadydone2 == 0 && ipart == 0) {
if (xthreeterm.toFixed(10) < 0) {
var alreadydone2 = 4
var p2 = Math.sqrt(xoneterm)
var q = Math.sqrt(xtwoterm)
var r = -g2 / (8*p2*q)
var s = bq2/(4*aq2)
} else {
var alreadydone2 = 5
var p2 = Math.sqrt(xoneterm.toFixed(10))
var q = Math.sqrt(xthreeterm.toFixed(10))
var r = -g2 / (8*p2*q)
var s = bq2/(4*aq2)
}
}
if (ipart != 0) {
var p2 = isquareroot(xtwoterm,ipart,0)
var p2ipart = isquareroot(xtwoterm,ipart,1)
var q = isquareroot(xthreeterm,-ipart,0)
var qipart = isquareroot(xthreeterm,-ipart,1)
var mult = calcmult(p2,p2ipart,q,qipart,0)
var r = -g2/(8*mult)
var s = bq2/(4*aq2)
}
if (ipart == 0 && xtwoterm.toFixed(10) < 0 && xthreeterm.toFixed(10) < 0) {
xtwoterm /= -1
xthreeterm /= -1
var p2 = 0
var q = 0
var p2ipart = Math.sqrt(xtwoterm)
var qipart = Math.sqrt(xthreeterm)
var mult = calcmult(p2,p2ipart,q,qipart,0)
var r = -g2/(8*mult)
var s = bq2/(4*aq2)
var ipart = 1
}
if (xoneterm.toFixed(10) > 0 && xtwoterm.toFixed(10) < 0 && xthreeterm.toFixed(10) == 0 && ipart == 0) {
xtwoterm /= -1
var p2 = Math.sqrt(xoneterm)
var q = 0
var p2ipart = 0
var qipart = Math.sqrt(xtwoterm)
var mult = calcmult(p2,p2ipart,q,qipart,0)
var mult2 = calcmult(p2,p2ipart,q,qipart,1)
var r = -g2/(8*mult)
if (mult2 != 0) {
var ripart = g2/(8*mult2)
var r = 0
}
var s = bq2/(4*aq2)
var ipart = 1
}
if (xtwoterm.toFixed(10) == 0 && xthreeterm.toFixed(10) == 0 && ipart == 0) {
var p2 = Math.sqrt(xoneterm)
var q = 0
var r = 0
var s = bq2/(4*aq2)
}
if (ipart == 0) {
document.solution.x1.value = ” ” + eval((p2 + q + r – s).toFixed(10))
document.solution.x2.value = ” ” + eval((p2 – q – r – s).toFixed(10))
document.solution.x3.value = ” ” + eval((-p2 + q – r – s).toFixed(10))
document.solution.x4.value = ” ” + eval((-p2 – q + r – s).toFixed(10))
document.solution.x1i.value = ” ” + 0
document.solution.x2i.value = ” ” + 0
document.solution.x3i.value = ” ” + 0
document.solution.x4i.value = ” ” + 0
}
if (perfect == 1) {
document.solution.x1.value = ” ” + -bq/4
document.solution.x2.value = ” ” + -bq/4
document.solution.x3.value = ” ” + -bq/4
document.solution.x4.value = ” ” + -bq/4
document.solution.x1i.value = ” ” + 0
document.solution.x2i.value = ” ” + 0
document.solution.x3i.value = ” ” + 0
document.solution.x4i.value = ” ” + 0
}
if (ipart == 0 && xtwoterm.toFixed(10) < 0 && xthreeterm.toFixed(10) < 0) {
xtwoterm /= -1
xthreeterm /= -1
var p2 = 0
var q = 0
var p2ipart = Math.sqrt(xtwoterm)
var qipart = Math.sqrt(xthreeterm)
var mult = calcmult(p2,p2ipart,q,qipart,0)
var r = -g2/(8*mult)
var s = bq2/(4*aq2)
var ipart = 1
}
if (xoneterm.toFixed(10) > 0 && xtwoterm.toFixed(10) < 0 && xthreeterm.toFixed(10) == 0 && ipart == 0) {
xtwoterm /= -1
var p2 = Math.sqrt(xoneterm)
var q = 0
var p2ipart = 0
var qipart = Math.sqrt(xtwoterm)
var mult = calcmult(p2,p2ipart,q,qipart,0)
var mult2 = calcmult(p2,p2ipart,q,qipart,1)
var r = -g2/(8*mult)
if (mult2 != 0) {
var ripart = g2/(8*mult2)
var r = 0
}
var s = bq2/(4*aq2)
var ipart = 1
}
if (xtwoterm.toFixed(10) == 0 && xthreeterm.toFixed(10) == 0 && ipart == 0) {
var p2 = Math.sqrt(xoneterm)
var q = 0
var r = 0
var s = bq2/(4*aq2)
}
if (ipart != 0) {
document.solution.x1.value = ” ” + eval((p2 + q + r – s).toFixed(10))
document.solution.x1i.value = ” ” + eval((p2ipart + qipart).toFixed(10))
document.solution.x2.value = ” ” + eval((p2 – q – r – s).toFixed(10))
document.solution.x2i.value = ” ” + eval((p2ipart – qipart).toFixed(10))
document.solution.x3.value = ” ” + eval((-p2 + q – r – s).toFixed(10))
document.solution.x3i.value = ” ” + eval((-p2ipart + qipart).toFixed(10))
document.solution.x4.value = ” ” + eval((-p2 – q + r – s).toFixed(10))
document.solution.x4i.value = ” ” + eval((-p2ipart – qipart).toFixed(10))
}
if (perfectbiquadratic == 1) {
document.solution.x1i.value = ” ” + eval(Math.sqrt(cq/2).toFixed(10))
document.solution.x2i.value = ” ” + eval(Math.sqrt(cq/2).toFixed(10))
document.solution.x3i.value = ” -” + eval(Math.sqrt(cq/2).toFixed(10))
document.solution.x4i.value = ” -” + eval(Math.sqrt(cq/2).toFixed(10))
document.solution.x1.value = ” ” + 0
document.solution.x2.value = ” ” + 0
document.solution.x3.value = ” ” + 0
document.solution.x4.value = ” ” + 0
}
}Head
Paste this code into the HEAD section of your HTML document.
<script type=”text/javascript” src=”quarticSolver.js”></script>Body
Paste this code into the BODY section of your HTML document.
<form name=”numbers2″>
<input type=”text” name=”a” size=5 value=””>x<sup>4</sup> + <input type=”text” name=”b” size=5 value=””>x<sup>3</sup> + <input type=”text” name=”c” size=5 value=””>x<sup>2</sup> + <input type=”text” name=”d” size=5 value=””>x + <input type=”text” name=”e” size=5 value=””> = 0 <input type=button value=”Solve” onclick=”extractcoefficents()”>
</form>
<br>
<form name=”solution”>
x<sub>1</sub>: <input type=”text” name=”x1″ size=23 value=””> + <input type=”text” name=”x1i” size=23 value=””> i<br>
x<sub>2</sub>: <input type=”text” name=”x2″ size=23 value=””> + <input type=”text” name=”x2i” size=23 value=””> i<br>
x<sub>3</sub>: <input type=”text” name=”x3″ size=23 value=””> + <input type=”text” name=”x3i” size=23 value=””> i<br>
x<sub>4</sub>: <input type=”text” name=”x4″ size=23 value=””> + <input type=”text” name=”x4i” size=23 value=””> i
</form>