document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152871>Question 152871</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many positive real solutions are there in f(x) = x^4 + 4x^3 + 6x^2 + 4x – 1<BR>\n" );
document.write( "Apply Descartes' Rule of Signs.<BR>\n" );
document.write( "a. 1<BR>\n" );
document.write( "b. 1 or 2<BR>\n" );
document.write( "c. 4 or 2<BR>\n" );
document.write( "d. 2 or 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112348 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=112348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Count the sign changes of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4%2B4x%5E3%2B6x%5E2%2B4x-1 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4%2B4x%5E3%2B6x%5E2%2B4x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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 no change in sign\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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 no change in sign\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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 no change in sign\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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 positive to negative \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there is 1 sign change for the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4%2B4x%5E3%2B6x%5E2%2B4x-1 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4%2B4x%5E3%2B6x%5E2%2B4x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there are 1 positive zeros\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the answer is a) 1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );