<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title></title>
<body>
<div align="center">例如输入:a=3, b=6, c=-123, d=-126 e=1080</div>
<form name="form1" action="">
ax<sup>4</sup> + bx<sup>3</sup> + cx<sup>2</sup> + dx + e = 0
<table border="0" align="center" colspan="4" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td><input type="text" name="aIn" size="5" placeholder="a">x<sup>4</sup> +</td>
<td><input type="text" name="bIn" size="5" placeholder="b">x³ +</td>
<td><input type="text" name="cIn" size="5" placeholder="c">x² +</td>
<td><input type="text" name="dIn" size="5" placeholder="d">x +</td>
<td><input type="text" name="eIn" size="5" placeholder="e">e</td>
</tr>
</tbody>
</table>
<center>
<input type="button" name="button1" value="计算" onclick="quad4solve(this.form)">
</center>
<table border="0" class="innerc" cellspacing="0" cellpadding="3">
<tbody>
<tr align="center">
<td class="inner" colspan="4"><b>结果:</b></td>
</tr>
<tr>
<td>x<sub>1</sub>:
<input type="text" name="x1Re" size="25"> +
<input type="text" name="x1Im" size="25"> i
</td>
</tr>
<tr>
<td>x<sub>2</sub>:
<input type="text" name="x2Re" size="25"> +
<input type="text" name="x2Im" size="25"> i
</td>
</tr>
<tr>
<td>x<sub>3</sub>:
<input type="text" name="x3Re" size="25"> +
<input type="text" name="x3Im" size="25"> i
</td>
</tr>
<tr>
<td>x<sub>4</sub>:
<input type="text" name="x4Re" size="25"> +
<input type="text" name="x4Im" size="25"> i
</td>
</tr>
</tbody>
</table>
</form>
<script type="text/javascript">
function quad4solve(dataForm)
{
var a = parseFloat(dataForm.aIn.value);
var b = parseFloat(dataForm.bIn.value);
var c = parseFloat(dataForm.cIn.value);
var d = parseFloat(dataForm.dIn.value);
var e = parseFloat(dataForm.eIn.value);
if (a == 0)
{
alert("The coefficient of the power four of x is 0. Please use the utility for a third degree quadratic.");
return;
}
if (e == 0)
{
alert("One root is 0. Now divide through by x and use the utility for a third degree quadratic to solve the resulting equation for the other three roots.");
return;
}
if (a != 1)
{
b /= a;
c /= a;
d /= a;
e /= a;
}
//立方解算器系数
var cb, cc, cd;
var discrim, q, r, RRe, RIm, DRe, DIm, dum1, ERe, EIm, s, t, term1, r13, sqR, y1, z1Re, z1Im, z2Re;
cb = -c;
cc = -4.0*e + d*b;
cd = -(b*b*e + d*d) + 4.0*c*e;
if (cd == 0)
{
alert("cd = 0.");
}
q = (3.0*cc - (cb*cb))/9.0;
r = -(27.0*cd) + cb*(9.0*cc - 2.0*(cb*cb));
r /= 54.0;
discrim = q*q*q + r*r;
term1 = (cb/3.0);
if (discrim > 0)
{
// 1 实数, 2 复数
s = r + Math.sqrt(discrim);
s = ((s < 0) ? -Math.pow(-s, (1.0/3.0)) : Math.pow(s, (1.0/3.0)));
t = r - Math.sqrt(discrim);
t = ((t < 0) ? -Math.pow(-t, (1.0/3.0)) : Math.pow(t, (1.0/3.0)));
y1 = -term1 + s + t;
}
else
{
if (discrim == 0)
{
r13 = ((r < 0) ? -Math.pow(-r,(1.0/3.0)) : Math.pow(r,(1.0/3.0)));
y1 = -term1 + 2.0*r13;
}
else
{
q = -q;
dum1 = q*q*q;
dum1 = Math.acos(r/Math.sqrt(dum1));
r13 = 2.0*Math.sqrt(q);
y1 = -term1 + r13*Math.cos(dum1/3.0);
}
}
// 确定了y1 分解立方的实根
term1 = b/4.0;
sqR = -c + term1*b + y1;
RRe = RIm = DRe = DIm = ERe = EIm = z1Re = z1Im = z2Re = 0;
if (sqR >= 0)
{
if (sqR == 0)
{
dum1 = -(4.0*e) + y1*y1;
if (dum1 < 0){
z1Im = 2.0*Math.sqrt(-dum1);
} else {
z1Re = 2.0*Math.sqrt(dum1);
z2Re = -z1Re;
}
}
else
{
RRe = Math.sqrt(sqR);
z1Re = -(8.0*d + b*b*b)/4.0 + b*c;
z1Re /= RRe;
z2Re = -z1Re;
}
}
else
{
RIm = Math.sqrt(-sqR);
z1Im = -(8.0*d + b*b*b)/4.0 + b*c;
z1Im /= RIm;
z1Im = -z1Im;
}
z1Re += -(2.0*c + sqR) + 3.0*b*term1;
z2Re += -(2.0*c + sqR) + 3.0*b*term1;
//At this point, z1 and z2 should be the terms under the square root for D and E
if (z1Im == 0)
{ // Both z1 and z2 real
if (z1Re >= 0)
{
DRe = Math.sqrt(z1Re);
}
else
{
DIm = Math.sqrt(-z1Re);
}
if (z2Re >= 0)
{
ERe = Math.sqrt(z2Re);
}
else
{
EIm = Math.sqrt(-z2Re);
}
}
else
{
r = Math.sqrt(z1Re*z1Re + z1Im*z1Im);
r = Math.sqrt(r);
dum1 = Math.atan2(z1Im, z1Re);
dum1 /= 2; //Divide this angle by 2
ERe = DRe = r*Math.cos(dum1);
DIm = r*Math.sin(dum1);
EIm = -DIm;
}
dataForm.x1Re.value = -term1 + (RRe + DRe)/2;
dataForm.x1Im.value = (RIm + DIm)/2;
dataForm.x2Re.value = -(term1 + DRe/2) + RRe/2;
dataForm.x2Im.value = (-DIm + RIm)/2;
dataForm.x3Re.value = -(term1 + RRe/2) + ERe/2;
dataForm.x3Im.value = (-RIm + EIm)/2;
dataForm.x4Re.value = -(term1 + (RRe + ERe)/2);
dataForm.x4Im.value = -(RIm + EIm)/2;
return;
}
</script>
</body>
</html>
Unquestionably believe that which you said. Your favorite justification seemed to be on the net the simplest thing to be
aware of. I say to you, I certainly get annoyed while people consider worries that they just don’t know about.
You managed to hit the nail upon the top as well as defined out the whole thing without having side
effect , people can take a signal. Will probably be back to
get more. Thanks
Now I am going away to do my breakfast, later than having my breakfast coming over again to read additional news.
Pretty section of content. I just stumbled upon your website and in accession capital to assert
that I get actually enjoyed account your blog posts.
Anyway I will be subscribing to your feeds and even I achievement you access consistently rapidly.
Awesome! Its genuinely remarkable paragraph, I have got much clear idea regarding from this article.
Hi there, I discovered your site by the use of Google
at the same time as searching for a comparable matter,
your website came up, it looks great. I’ve bookmarked it in my google bookmarks.
Hi there, simply changed into alert to your blog thru Google, and located that
it’s truly informative. I’m going to be careful for brussels.
I’ll appreciate in the event you continue this in future.
A lot of people will probably be benefited out of your writing.
Cheers!