document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885523>Question 885523</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535221 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=535221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the equation is 7th degree then it has 7 roots.<BR>\n" );
document.write( "those roots can be complex or real.<BR>\n" );
document.write( "complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one.<BR>\n" );
document.write( "in other words, if one complex root is a + bi, then the other complex root is a - bi.<BR>\n" );
document.write( "if at least one root is complex, then you would have a minimum of 2 complex roots with a maximum of 5 real roots.<BR>\n" );
document.write( "the equation can have at most 6 complex roots (3 pairs) so the minimum number of real roots is equal to 1.\r<BR>\n" );
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