document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145104>Question 145104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many positive real soulutions are there in x^4-4x^3+6x^2-4x+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105796 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=105796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's count the sign changes of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4-4x%5E3%2B6x%5E2-4x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-4x%5E3%2B6x%5E2-4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4 ALIGN=MIDDLE  ALT=\"x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E3 ALIGN=MIDDLE  ALT=\"-4x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a sign change from positive to negative \r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E3 ALIGN=MIDDLE  ALT=\"-4x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2 ALIGN=MIDDLE  ALT=\"6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a sign change from negative to positive \r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2 ALIGN=MIDDLE  ALT=\"6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x ALIGN=MIDDLE  ALT=\"-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a sign change from positive to negative \r<BR>\n" );
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document.write( "From <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=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a sign change from negative to positive \r<BR>\n" );
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document.write( "So there are 4 sign changes for the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4-4x%5E3%2B6x%5E2-4x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-4x%5E3%2B6x%5E2-4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So there are 4, 2, or 0 positive zeros (remember to count down by 2's)\r<BR>\n" );
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