document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631907>Question 631907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P(x)=x^5+x^3+8x^2+8, Find ALL zeros of P(x). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397895 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=397895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(x)=x^5+x^3+8x^2+8, Find ALL zeros of P(x).<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Use rational roots theorem to solve: \r<BR>\n" );
document.write( "\n" );
document.write( "...0...|.....1.......0.......1........8......0........8<BR>\n" );
document.write( "...1..|......1.......1.......2.......10....10.....18 (1 is upper limit, all numbers>0) <BR>\n" );
document.write( "============================<BR>\n" );
document.write( "...0...|.....1.......0.......1.......8......0.........8<BR>\n" );
document.write( ".-1...|.....1.....-1.......2.......6.....-6........2  <BR>\n" );
document.write( ".-2...|.....1.....-2.......3.......2.....-4........0 (-2 is a root)<BR>\n" );
document.write( ".-3...|.....1.....-3.......8....-16.....48.....-144 (-3 is lower limit, numbers alternate in sign)<BR>\n" );
document.write( "P(x)=(x+2)(x^4-2x^3+3x^2+2x-4)<BR>\n" );
document.write( "Function has only one real zero=-2.<BR>\n" );
document.write( "Other 4 zeros are 2 pairs of non-real or imaginary roots. (complex conjugates)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );