Print - JavaScript Quartic Equation Solver - JavaScriptBank.com

This simple JavaScript code example can solve quartic equations in the form of ax^4 + bx+3 + cx^2 + dx + e = 0. Another way to get answers but do not want to calculate more.

JavaScript
`<script type="text/javascript">// Created by: Brian Kieffer | http://www.freewebs.com/brianjs/// This script downloaded from www.JavaScriptBank.comfunction 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  }}</script>`

HTML
`<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>`