document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534404>Question 534404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many positive real zeros does the function f(x) = x4 + x3 – 7x – 1 have?<BR>\n" );
document.write( "a) 3 or 1<BR>\n" );
document.write( "B) 1<BR>\n" );
document.write( "c) 2 or 0<BR>\n" );
document.write( "d) 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351497 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=351497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <B>Check my profile and contact me for one on one online tutoring.</B><P>\r<BR>\n" );
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document.write( "List the signs of the coefficients of each term.  That is, the signs of the numbers in front of the x^n and the constant.  The max number of positive real roots is either the number of sign changes, or the number of sign changes decreased by a multiple of 2.<P><BR>\n" );
document.write( "Make sure the polynomial is written in decreasing order of exponents.  That is ^n , ^(n-1), ^(n-2)...<BR>\n" );
document.write( "x^4 + x^3 – 7x – 1  has coefficients 1, 1 -7 -1.  The signs are:<br><BR>\n" );
document.write( "+, +, -, -  There is one sign change (from + to -), therefore the maximum number of positive real roots is 1 or -1 0r -3 or...  <P><BR>\n" );
document.write( "There can't be a negative number of positive real roots.  So the answer is 1.<P><BR>\n" );
document.write( "This is Descartes Rule of Signs.<BR>\n" );
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