document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88391>Question 88391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I am havign soem issues with understanding the Descartes rule of signs and am unsure of how to solve the problem.\r<BR>\n" );
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document.write( "Use Descartes rule of signs to discuss the possibilities for the roots to each equation. Do not solve it.<BR>\n" );
document.write( "2x^3-3x^2-5x-9=0\r<BR>\n" );
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document.write( "Here is what I have tried to do \r<BR>\n" );
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document.write( "2(-x)^3 - 3(-x)^2-5(-x)-9=-2x^3-3x^2-5x-9\r<BR>\n" );
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document.write( "How do I tell how many roots there are to this problem? <BR>\n" );
document.write( "Thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64202 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=64202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x^3 - 3x^2 - 5x - 9 = f(x)<BR>\n" );
document.write( "The sign of the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > determines the sign of the roots.<BR>\n" );
document.write( "2x^3 - 3x^2 - 5x - 9 = f(+x)<BR>\n" );
document.write( "(+) (-) (-) (-) from a positive 2, a negative 3, a negative 5, and a negative 9<BR>\n" );
document.write( "The sign changes once.<BR>\n" );
document.write( "Root Types:<BR>\n" );
document.write( "Pos: 1<BR>\n" );
document.write( "Neg: ~<BR>\n" );
document.write( "Img: ~<BR>\n" );
document.write( "-2x^3 - 3x^2 + 5x - 9 = f(-x)<BR>\n" );
document.write( "(-) (-) (+) (-)<BR>\n" );
document.write( "The sign changes twice.<BR>\n" );
document.write( "Root Types:<BR>\n" );
document.write( "Pos: 1<BR>\n" );
document.write( "Neg: 2<BR>\n" );
document.write( "Img: ~<BR>\n" );
document.write( "There are only three roots because of the type of equation, so the imaginery choice is zero. A rule is that two can be taken from a type and added for imaginery.<BR>\n" );
document.write( "Root Types:<BR>\n" );
document.write( "Pos: 1 .. 1<BR>\n" );
document.write( "Neg: 2 .. 0<BR>\n" );
document.write( "Img: 0 .. 2<BR>\n" );
document.write( "~ How to Determine Maximum Amount of Roots ~<BR>\n" );
document.write( "1 Root<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C2%2C-2%2C2%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C2%2C-2%2C2%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2 Roots<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C2%2C-2%2C2%2C%28x+-+1%29x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C2%2C-2%2C2%2C%28x+-+1%29x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3 Roots ~ Max.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C2%2C-2%2C2%2C-2x%5E3+%2B+5x%5E2+-+3x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C2%2C-2%2C2%2C-2x%5E3+%2B+5x%5E2+-+3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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