document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63740>Question 63740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help?\r<BR>\n" );
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document.write( "Use Descartes' Rule of Signs to find the number of possible number of positive zeros and the possible number of negative zeros of Q(x)=x^42x^3+4x^2-3x-2.\r<BR>\n" );
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document.write( "Find the horizontal and vertical asymptotes of the function f(x)=x^2+3x-2/x-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46288 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE THE FOLLOWING EXAMPLE AND TRY..<BR>\n" );
document.write( "Using Descartes Rule of Signs to determine how many<BR>\n" );
document.write( "positive and how many negative real zeros the<BR>\n" );
document.write( "polynomial functions may have. Do not attempt to find<BR>\n" );
document.write( "the zeros.<BR>\n" );
document.write( "f(x)=x^6-4x^5-x^4-3x^3+3x^2+x+4<BR>\n" );
document.write( "Thank You.<BR>\n" );
document.write( "TO FIND NUMBER OF POSSIBLE POSITIVE ROOTS..<BR>\n" );
document.write( "1.WRITE F(X) IN DESCENDING ORDER..<BR>\n" );
document.write( "IT IS ALREADY WRITTEN HERE.<BR>\n" );
document.write( "2.FIND NUMBER OF CHANGES IN SIGNS OF COEFFICIENTS OF<BR>\n" );
document.write( "TERMS OF F(X)..<BR>\n" );
document.write( "THERE ARE 2 CHANGES ...+1X^6 TO -4X^5...AND...-3X^3 TO<BR>\n" );
document.write( "+3X^2.<BR>\n" );
document.write( "HENCE THERE WILL BE A MAXIMUM OF 2 POSITIVE ROOTS.<BR>\n" );
document.write( "NEXT TO FIND THE NUMBER OF POSSIBLE NEGATIVE ROOTS..<BR>\n" );
document.write( "1.WRITE F(-X) IN DESCENDING ORDER..<BR>\n" );
document.write( "IT IS ...<BR>\n" );
document.write( "F(-X)= X^6+4X^5-X^4+3X^3+3X^2-X+4<BR>\n" );
document.write( "2.FIND NUMBER OF CHANGES IN SIGNS OF COEFFICIENTS OF<BR>\n" );
document.write( "TERMS OF F(-X)..<BR>\n" );
document.write( "THERE ARE 3 CHANGES ...+4X^5 TO -X^4...AND...-X^4 TO<BR>\n" );
document.write( "+3X^3....AND<BR>\n" );
document.write( "+3X^2 TO -X<BR>\n" );
document.write( "HENCE THERE WILL BE A MAXIMUM OF 3 NEGATIVE ROOTS.<BR>\n" );
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document.write( "Find the horizontal and vertical asymptotes of the function f(x)=x^2+3x-2/x-4<BR>\n" );
document.write( "HOPE YOU MEAN ... f(x)=(x^2+3x-2)/(x-4)..IF YOU DONT PUT BRACKETS IT MAY MEAN ANY THING LIKE.....f(x)=x^2+3x-[2/x]-4..ETC..ANY WAY TAKING AS MENTIONED<BR>\n" );
document.write( " F(X) = Y = (X-2)(X-1)/(X-4)<BR>\n" );
document.write( "VERTICAL ASYMPTOTE...<BR>\n" );
document.write( "FIND WHEN Y WILL TEND TO INFINITY?<BR>\n" );
document.write( "AS X TENDS TO 4 , Y TENDS TO INFINITY. HENCE X-4=0...OR...X=4 IS THE VERTICAL ASYMPTOTE. <BR>\n" );
document.write( "HORIZONTAL ASYMPTOTE...<BR>\n" );
document.write( "FIND WHETHER Y WILL TEND TO A FINITE LIMIT WHEN X TENDS TO + OR - INFINITY?<BR>\n" );
document.write( "WE FIND THAT Y TENDS TO INFINITY AS X TENDS TO INFINITY ..HENCE THERE <BR>\n" );
document.write( "ARE NO HORIZONTAL ASYMPTOTES\r<BR>\n" );
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document.write( " </SPAN>\n" );
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