document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252551>Question 252551</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let P and Q be polynomials such that P(x) and Q(P(Q(x))) have the same roots. If<BR>\n" );
document.write( "the degree of P is 7, what is the degree of Q? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184539 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=184539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let P(x) = X^7 and Q(x) = X.<BR>\n" );
document.write( "Right now the real roots of P(x) = 0.<BR>\n" );
document.write( "P(Q(x)) = X^7<BR>\n" );
document.write( "Q(P(Q((x))) = x^7. <BR>\n" );
document.write( "The roots of Q(P(Q(x))) = 0.<BR>\n" );
document.write( "So it appears that the degree of Q = 1.\r<BR>\n" );
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document.write( "In general, if the roots are both 0, then the degree of Q >=1, hypothesis. <BR>\n" );
document.write( "We could try to generalize this but that may take more time than what is necessary.\r<BR>\n" );
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document.write( "Hope this helps.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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