document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=400662>Question 400662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^6-9x^3-10=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #283603 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=283603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+x%5E3 ALIGN=MIDDLE  ALT=\"z+=+x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that we can obtain a quadratic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+-+9z+-+10+=+0 ALIGN=MIDDLE  ALT=\"z%5E2+-+9z+-+10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z-10%29%28z%2B1%29+=+0 ALIGN=MIDDLE  ALT=\"%28z-10%29%28z%2B1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "z = 10, z = -1. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+x%5E3 ALIGN=MIDDLE  ALT=\"z+=+x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+10 ALIGN=MIDDLE  ALT=\"x%5E3+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+-1 ALIGN=MIDDLE  ALT=\"x%5E3+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Each of these equations has three complex roots that form roots of unity. For the first equation, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+root%283%2C+10%29 ALIGN=MIDDLE  ALT=\"x+=+root%283%2C+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5+%2B-+5sqrt%283%29i ALIGN=MIDDLE  ALT=\"x+=+5+%2B-+5sqrt%283%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The second equation has roots <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F2+%2B-+%28sqrt%283%29%2F2%29i ALIGN=MIDDLE  ALT=\"x+=+1%2F2+%2B-+%28sqrt%283%29%2F2%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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