document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38459>Question 38459</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131808583/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> find the number of complex roots,the possible number of real rational roots\r<BR>\n" );
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document.write( "x^7-2x^6+3x^2-2x+5=0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "8-4x^3+4x^6=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24134 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24134\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^7-2x^6+3x^2-2x+5=0\r<BR>\n" );
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document.write( "The highest power of x is 7.  This is the degree or order of the equation.  It also tells you that there are a total of 7 roots, if you include real roots, complex roots, and repeated roots.  Complex roots will always be in conjugate pairs--i.e., two or four or six complex roots.  Therefore, these are the possibilites.\r<BR>\n" );
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document.write( "7 real and no complex roots<BR>\n" );
document.write( "5 real and two complex roots (one conjugate pair).<BR>\n" );
document.write( "3 real and four complex roots (two conjugate pairs).<BR>\n" );
document.write( "1 real and six complex roots (three conjugate pairs).\r<BR>\n" );
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document.write( "8-4x^3+4x^6=0\r<BR>\n" );
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document.write( "The highest power of x is 6, so there will be a total of 6 roots.  These are the possibilities:\r<BR>\n" );
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document.write( "6 real roots and no complex roots<BR>\n" );
document.write( "4 real roots and two complex roots (1 conjugate pair)<BR>\n" );
document.write( "2 real and four complex roots (two conjugate pairs).<BR>\n" );
document.write( "No real and six complex roots (three conjugate pairs).\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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document.write( " </SPAN>\n" );
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