document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472568>Question 472568</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros of:\r<BR>\n" );
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document.write( "f(x)= x^5 - 3x^4 - 2x^3 + x^2 +5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324054 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since there are 2 variations of signs, there are 0 or 2 positive real zeros.<BR>\n" );
document.write( "If x is replaced by -x, the resulting polynomial is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E5+-+3x%5E4+%2B+2x%5E3+%2B+x%5E2+%2B+5 ALIGN=MIDDLE  ALT=\"-x%5E5+-+3x%5E4+%2B+2x%5E3+%2B+x%5E2+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which has 1 variation of sign, hence exactly one negative zero.  Hence, either there are <BR>\n" );
document.write( "(i) 2 positive, 1 negative, and 2 complex zeros, \r<BR>\n" );
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document.write( "OR\r<BR>\n" );
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document.write( "(ii) 0 positive, 1 negative, and 4 complex zeros. </SPAN>\n" );
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