document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037884>Question 1037884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A polynomial function f((x) of degree 4 with real coefficients has zeros of 3 and 5-i. Explain why one of the remaining zeros must be a real number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652545 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A polynomial function f((x) of degree 4 with real coefficients has zeros of 3 and 5-i. Explain why one of the remaining zeros must be a real number.<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Complex zeroes occur in pairs --> 5+i is a zero.<BR>\n" );
document.write( "That's 3.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "A 4th complex zero would mean its conjugate would make 5 zeroes.<BR>\n" );
document.write( "--> has to be real. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );