document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=431581>Question 431581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am on break and can't get help from my math teacher, I need to answer a question using these two functions f(x)=x^5-x^4+40x^2-x-39 and h(x)=2x^4+7x^3-3x^2-14x-6<BR>\n" );
document.write( "How many roots do f(x) and h(x) each have in the complex numbers? Help is greatly appreciated.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299470 by </B><A HREF=/tutors/aboutme.mpl?userid=tinbar><B>tinbar(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tinbar><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=299470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in general, using the fundamental theorem of algebra, you can conclude that any polynomial of degree n has n solutions (including multiplicity(order)) of the roots.\r<BR>\n" );
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document.write( "ex: g(x) = x^2 + 1. This has no solutions in real numbers, but by the fund thm of algebra, they have 2 solutions in complex numbers; namely x=i and x=-i, where i = sqrt(-1)\r<BR>\n" );
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document.write( "ex: p(x) = x^2+2i+1. This has 1 solution in the complex numbers, x=i, but it has order 2, therefore it satisfies the fund thm of algebra\r<BR>\n" );
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document.write( "can you now name how many solutions your functions will have in complex numbers? </SPAN>\n" );
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