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<! Made by Html Translation Ver 1.0><html><head><title> 多项式的根 </title></head><body BACKGROUND="../img1/bg0000.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/bg0000.gif"><script language="JAVASCRIPT"><!--if (navigator.onLine){document.write("<!-- Spidersoft WebZIP Ad Banner Insert -->");document.write("<TABLE width=100% border=0 cellpadding=0 cellspacing=0>");document.write("<TR>");document.write("<TD>");document.write("<ILAYER id=ad1 visibility=hidden height=60></ILAYER>");document.write("<NOLAYER>");document.write("<IFRAME SRC='http://www.spidersoft.com/ads/bwz468_60.htm' width=100% height=60 marginwidth=0 marginheight=0 hspace=0 vspace=0 frameborder=0 scrolling=no></IFRAME>");document.write("</NOLAYER>");document.write("</TD>");document.write("</TR>");document.write("</TABLE>");document.write("<!-- End of Spidersoft WebZIP Ad Banner Insert-->");} //--></script><!-- Spidersoft WebZIP Ad Banner Insert --><!-- End of Spidersoft WebZIP Ad Banner Insert--><font COLOR="#0000FF"><h1>8.1 多项式的根</h1></font><hr><p>一个多项式视其阶数而定，它的根可以有一个到数个，可能为实数也可能是复数。要求一高阶多项式的根往 往须借助数值方法，所幸<font FACE="Times New Roman">MATLAB</font>已将这些数值方法写成一函数<font COLOR="#FF0000" FACE="Times New Roman">roots(p)</font>，我们只要输入多项式的各阶系数（ 以 <font COLOR="#FF0000" FACE="Times New Roman">p</font><font FACE="Times New Roman"> </font>代表）即可求解到对应的根。 </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> p=[1 3 2];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> r=roots(p)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">r =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-2</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-1</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> p=[1 -12 0 25 116]; % </font><font COLOR="#FF0000">注意二阶项系数为零须要输入，否则多项式的阶数就不对</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> r=roots(p) % </font><font COLOR="#FF0000">有实数根及复数根</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">r =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">11.7473</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">2.7028</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-1.2251 + 1.4672i</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-1.2251 - 1.4672i <br></font></p><p>与 <font COLOR="#FF0000" FACE="Times New Roman">roots</font><font FACE="Times New Roman"> </font>相关的函数尚有 <font COLOR="#FF0000" FACE="Times New Roman">poly</font><tt><font FACE="Courier New">, </font></tt><font COLOR="#FF0000" FACE="Times New Roman">real</font>，这二个函数的用途是要验算求解的根展开能求得原多项式。 例如有一个二次方程式的根为<font FACE="Times New Roman">2, 1</font>，则以下式计算原多项式 </p><p><img SRC="../img8/img00001.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img8/img00001.gif" WIDTH="240" HEIGHT="26"> </p><p><font COLOR="#FF0000" FACE="Times New Roman">poly</font><font FACE="Times New Roman"> </font>函数就是在求出多项式的各阶系数，其语法为 <font COLOR="#FF0000" FACE="Times New Roman">poly(r)</font>，其中 <font COLOR="#FF0000" FACE="Times New Roman">r</font><font FACE="Times New Roman"> </font>是代表根的阵列。而 <font COLOR="#FF0000" FACE="Times New Roman">real</font><font FACE="Times New Roman"> </font>则是用来去除因计算时产生的假虚部系数，为何会有此种情形请参考以下的例子。 </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> r=[-2 1];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> pp=poly(r) % pp=(x+2)(x-1)=x^2+3x+2</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">pp =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">1 3 2</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> p=[1 -4 6 -4];</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> r=roots(p)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">r =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">2.0000 1.0000 + 1.0000i 1.0000 - 1.0000i </font></p><p><font COLOR="#FF0000" FACE="Times New Roman">>> pp=poly(r) % </font><font COLOR="#FF0000">这个多项式的系数与原多项式 </font><font COLOR="#FF0000" FACE="Times New Roman">p </font><font COLOR="#FF0000">相同</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">pp =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">1 -4 6 -4</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> pp=[1 7 12 9]; % </font><font COLOR="#FF0000">再看另一个多项式</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> r=roots(pp)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">r =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-4.9395 </font></p><p><font COLOR="#FF0000" FACE="Times New Roman">-1.0303 + 0.8721i</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-1.0303 - 0.8721i</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> pp=poly(r) % </font><font COLOR="#FF0000">注意因计算的误差会有假虚部产生</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">pp =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">1.0000 7.0000 12.0000 9.0000 + 0.0000i</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>> pp=real(pp) % </font><font COLOR="#FF0000">可以</font><font COLOR="#FF0000" FACE="Times New Roman">real</font><font COLOR="#FF0000">将假虚部去除，将原多项式还原</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">pp =</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">1.0000 7.0000 12.0000 9.0000<br></font></p><hr><a HREF="ch8.htm" tppabs="http://webclass.ncu.edu.tw/~junwu/ch8.htm"><p><img SRC="../img1/lastpage.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/lastpage.gif" BORDER="0" WIDTH="42" HEIGHT="42"></a> <a HREF="ch8_2.htm" tppabs="http://webclass.ncu.edu.tw/~junwu/ch8_2.htm"><img SRC="../img1/nextpage.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/nextpage.gif" BORDER="0" HSPACE="10" WIDTH="42" HEIGHT="42"></a> <a HREF="../index.html" tppabs="http://webclass.ncu.edu.tw/~junwu/index.html"><img SRC="../img1/outline.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/outline.gif" BORDER="0" HSPACE="6" WIDTH="42" HEIGHT="42"></a><br><font SIZE="2" COLOR="#AA55FF">上一页 下一页 讲义大纲 </font><layer src="http://www.spidersoft.com/ads/bwz468_60.htm" visibility="hidden" id="a1" width="600" onload="moveToAbsolute(ad1.pageX,ad1.pageY); 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