document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92096>Question 92096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros for the function P(x) = -3x^5 -7x^3 -4x - 5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66953 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=66953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "First lets find the number of possible positive real zeros:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E5-7x%5E3-4x-5 ALIGN=MIDDLE  ALT=\"-3x%5E5-7x%5E3-4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simply count the sign changes\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "By looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E5-7x%5E3-4x-5 ALIGN=MIDDLE  ALT=\"-3x%5E5-7x%5E3-4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that there are no sign changes (all the terms are negative).\r<BR>\n" );
document.write( "\n" );
document.write( "So there are no positive zeros\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now lets find the number of possible negative real zeros\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------\r<BR>\n" );
document.write( "\n" );
document.write( "First we need to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29 ALIGN=MIDDLE  ALT=\"f%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29=-3%28-x%29%5E5-7%28-x%29%5E3-4%28-x%29-5 ALIGN=MIDDLE  ALT=\"f%28-x%29=-3%28-x%29%5E5-7%28-x%29%5E3-4%28-x%29-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in -x (just replace every x with -x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29=3x%5E5%2B7x%5E3%2B4x-5 ALIGN=MIDDLE  ALT=\"f%28-x%29=3x%5E5%2B7x%5E3%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify (note: if the exponent of the given term is odd, simply negate the sign of the term)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29=3x%5E5%2B7x%5E3%2B4x-5 ALIGN=MIDDLE  ALT=\"f%28-x%29=3x%5E5%2B7x%5E3%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Now lets count the sign changes for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E5%2B7x%5E3%2B4x-5 ALIGN=MIDDLE  ALT=\"3x%5E5%2B7x%5E3%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "Here is the list of sign changes:\r<BR>\n" );
document.write( "\n" );
document.write( "<ol><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (positive to negative)</li></ol>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E5%2B7x%5E3%2B4x-5 ALIGN=MIDDLE  ALT=\"3x%5E5%2B7x%5E3%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > there are a maximum of 1 negative zero\r<BR>\n" );
document.write( "\n" );
document.write( "So there is exactly one negative zero\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Summary:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there are  0 positive zeros  and  1 negative zero </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );