document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31163>Question 31163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine if the polynomial below is irreducible over Q(rationals)<BR>\n" );
document.write( "t^5 - 15t^4 + 18t^2 -12  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18010 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=18010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine if the polynomial below is irreducible over Q(rationals)<BR>\n" );
document.write( "t^5 - 15t^4 + 18t^2 -12 <BR>\n" );
document.write( "THE RULE FOR EXISTENCE OF RATIONAL ROOTS IS <BR>\n" );
document.write( "P/Q WILL BE A ROOT ONLY IF P IS A FACTOR OF CONSTANT TERM (-12 HERE)AND Q IS A FACTOR OF HIGHEST DEGREE TERM'S COEFFICIENT (1 HERE)<BR>\n" );
document.write( "SO ONLY POSSIBLE RATIONAL ROOTS ARE 1,2,3,4,6,12,-1,-2,-3,-4,-6,-12......<BR>\n" );
document.write( "WE FIND THAT NONE OF THEM YIELD A ZERO THAT IS F(1)..OR..F(2)....ETC ARE NOT ZERO.HENCE THERE ARE NO RATIONAL ROOTS FOR THIS EQN. </SPAN>\n" );
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