document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197352>Question 197352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^4-4x^3-4x^2+16x-32=0\r<BR>\n" );
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document.write( "this problem is really stumping me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147971 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=147971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "And with good reason.  Using the Rational Zero Theorem, the potential rational zeros of your equation are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \pm 1, \pm 2, \pm 4, \pm 8, \pm 16, \pm 32\">\r<BR>\n" );
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document.write( "I used an Excel spreadsheet to perform synthetic division on all 12 potential zeros and none of them worked.  That means you either have 4 real/irrational zeros, 2 real/irrational and 2 complex, or 4 complex zeros.  Using a graphing program I determined that it is the 2 and 2 situation.\r<BR>\n" );
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document.write( "The only way to solve this puppy is to use the general solution of the quartic equation.  Of course, that is a computational horror that I wouldn't wish on anybody -- even if I didn't like them very well.  Furthermore, I'm not going to attempt it here.\r<BR>\n" );
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document.write( "If you are really interested, go to http://en.wikipedia.org/wiki/Quartic_equation\r<BR>\n" );
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document.write( "Scroll down to 'Summary of Ferrari's Method' and then follow the steps outlined.  And good luck to you.  By the way, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \beta \neq 0\"> so this one is as difficult as it gets.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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