<!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>
I was suggested this website by my cousin. I’m not sure whether this post is written by him as no one else know such detailed about my trouble.
You are wonderful! Thanks!
Thanks on your marvelous posting! I definitely enjoyed reading it, you might be a great author.I
will be sure to bookmark your blog and may come back in the future.
I want to encourage you to ultimately continue your great posts,
have a nice day!
Appreciate the recommendation. Will try
it out.
Great goods from you, man. I’ve understand your stuff previous to and you’re just too magnificent.
I actually like what you have acquired here, certainly
like what you’re stating and the way in which you say it.
You make it enjoyable and you still care for to keep it smart.
I can’t wait to read far more from you. This is
really a great website.
Woah! I’m really loving the template/theme of this website.
It’s simple, yet effective. A lot of times it’s challenging to get that “perfect balance” between superb usability and
appearance. I must say you have done a awesome job with this.
In addition, the blog loads super fast for me on Internet explorer.
Outstanding Blog!