<!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>
Good answers in return of this query with solid arguments and describing
all about that.
Excellent post. I was checking continuously this blog and I am inspired!
Extremely helpful info particularly the ultimate phase 🙂 I care
for such information much. I was seeking this particular info for a very long time.
Thank you and good luck.
Heya i am for the first time here. I came across this board and I find It really useful & it helped me out
a lot. I hope to give something back and aid others like you helped me.
Hi, yeah this article is really fastidious and I have learned lot of
things from it about blogging. thanks.
Undeniably believe that which you said. Your favourite justification seemed to be on the internet the
simplest thing to have in mind of. I say to you, I definitely get
annoyed even as folks think about concerns that they plainly don’t realize about.
You controlled to hit the nail upon the top and also defined out the whole thing without having side-effects ,
folks could take a signal. Will likely be again to get more.
Thank you