document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177951>Question 1177951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the possible rational zeros and then find all the zeros of the polynomial function: f(x)=x⁴+8x³+19x²+12x-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807126 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807126\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The only possible rational roots are of the form (plus or minus) p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.  So in this polynomial the only possible rational roots are -2, -1, 1, and 2.<br><BR>\n" );
document.write( "Simple quick substitution shows that none of those are roots.<br><BR>\n" );
document.write( "It is a 4th degree polynomial, so there are 4 roots; and we now know they are all irrational.  So they can only be determined approximately by numerical methods such as calculus or a graphing calculator.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );