document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134148>Question 1134148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Indentify the number of positive, negative, and imaginary roots, all rational roots , and the total amount of roots.<BR>\n" );
document.write( "x^3+x-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 #751425 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bx-6=0+ ALIGN=MIDDLE  ALT=\"x%5E3%2Bx-6=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=>  the highest degree of its monomial (individual term) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this function will have  one to three roots\r<BR>\n" );
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document.write( "use the Newton-Raphson method:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bn%2B1%5D ALIGN=MIDDLE  ALT=\"x%5Bn%2B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bn%5D ALIGN=MIDDLE  ALT=\"x%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%5Bn%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5Bn%5D%29\"   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=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Bn%5D%29=3x%5E2%2B1 ALIGN=MIDDLE  ALT=\"%28x%5Bn%5D%29=3x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "let  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B0%5D=5 ALIGN=MIDDLE  ALT=\"x%5B0%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "compute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bn%2B1%5D ALIGN=MIDDLE  ALT=\"x%5Bn%2B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > until \Delta \:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bn%2B1%5D+%3C+0.000001 ALIGN=MIDDLE  ALT=\"x%5Bn%2B1%5D+%3C+0.000001\"   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=f%28x%5B0%5D%29=5%5E3%2B5-6=124 ALIGN=MIDDLE  ALT=\"f%28x%5B0%5D%29=5%5E3%2B5-6=124\"   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=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B0%5D%29=3%2A5%5E2%2B1=76 ALIGN=MIDDLE  ALT=\"%28x%5B0%5D%29=3%2A5%5E2%2B1=76\"   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=x%5B1%5D=5-124%2F76 ALIGN=MIDDLE  ALT=\"x%5B1%5D=5-124%2F76\"   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=x%5B1%5D=5-124%2F76 ALIGN=MIDDLE  ALT=\"x%5B1%5D=5-124%2F76\"   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=x%5B1%5D=3.36842 ALIGN=MIDDLE  ALT=\"x%5B1%5D=3.36842\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " &Delta;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=5-3.36842 ALIGN=MIDDLE  ALT=\"x%5B1%5D=5-3.36842\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " &Delta;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=highlight%281.6344%29 ALIGN=MIDDLE  ALT=\"x%5B1%5D=highlight%281.6344%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> one real root\r<BR>\n" );
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document.write( "Apply long division:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%2Bx-6%29%2F%28x-1.6344%29+=x%5E2%2B1.6344x%2B3.67115 ALIGN=MIDDLE  ALT=\"%28x%5E3%2Bx-6%29%2F%28x-1.6344%29+=x%5E2%2B1.6344x%2B3.67115\"   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=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   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=x+=+%28-1.6344+%2B-+sqrt%28+1.6344%5E2-4%2A1%2A3.67115+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1.6344+%2B-+sqrt%28+1.6344%5E2-4%2A1%2A3.67115+%29%29%2F%282%2A1%29+\"   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=x+=+%28-1.6344+%2B-+sqrt%28+-12.01333664+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1.6344+%2B-+sqrt%28+-12.01333664+%29%29%2F2+\"   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=x+=+%28-1.6344+%2B-+3.466%2Ai%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1.6344+%2B-+3.466%2Ai%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "other roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1.6344+%2B+3.466%2Ai%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1.6344+%2B+3.466%2Ai%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B2%5D+=-0.8172%2B1.733%2Ai%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B2%5D+=-0.8172%2B1.733%2Ai%29\"   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=x+=+%28-1.6344+-+3.466%2Ai%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1.6344+-+3.466%2Ai%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B3%5D+=-0.8172+-1.733%2Ai%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B3%5D+=-0.8172+-1.733%2Ai%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );