document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=430001>Question 430001</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the polynomial P(x)=2x^3+5x^2-3x-4\r<BR>\n" );
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document.write( "A. Use Descartes' Rule to analyze the zeros of the function.<BR>\n" );
document.write( "B. Use the Rational Zeros Theorem to identify the possible rational zeros.\r<BR>\n" );
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document.write( "I am really having a hard time figuring this out, I would appreciate any help on this! <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298627 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=298627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Descartes Rule of Signs:  Remembering that the lead coefficient, lacking a minus sign, is a positive coefficient, step from one term to the other counting the number of times the sign changes from + to - or - to +.\r<BR>\n" );
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document.write( "I count 1.  Therefore there is exactly 1 positive root.\r<BR>\n" );
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document.write( "If you replace x with -x, you get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(-x)\ =\ -2x^3\ +\ 5x^2\ +\ 3x\ -\ 4\">\r<BR>\n" );
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document.write( "And then you count two sign changes.  Hence there are exactly 2 or 0 negative roots.\r<BR>\n" );
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document.write( "The rational roots theorem says the possible rational roots are all rational numbers of the form \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \pm\frac{p}{q}\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is an integer divisor of the constant term and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q\"> is an integer divisor of the lead coefficient.\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \pm1,\ \pm2,\ \pm4,\ \pm\frac{1}{2}\">\r<BR>\n" );
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document.write( "are your possible rational roots.\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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