document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154820>Question 1154820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Descartes rule of signs to find the possible positive, negative, and imaginary zeroes for:<BR>\n" );
document.write( "x^5 − 3x^4 + x^3 − 4x^2 + 5x − 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777334 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=777334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "With the polynomial in standard form (in decreasing powers of the variable), there are 5 sign changes.  So the number of positive real roots is 5, or 3, or 1.<br><BR>\n" );
document.write( "Replacing \"x\" with \"-x\" in the polynomial results in a polynomial with 0 sign changes, so there are no negative real roots.<br><BR>\n" );
document.write( "A graph shows that in fact there are 3 positive real roots, which means there is 1 pair of imaginary roots.<br><BR>\n" );
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document.write( " </SPAN>\n" );
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