Full version: jsB@nk » Calculation » Math » JavaScript Quartic Equation Solver
URL: https://www.javascriptbank.com/javascript-quartic-equation-solver.html
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.
Full version: jsB@nk » Calculation » Math » JavaScript Quartic Equation Solver
URL: https://www.javascriptbank.com/javascript-quartic-equation-solver.html
<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><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>