document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=46791>Question 46791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A polynomial g(x) of degree 5 whose coefficients are real numbers has zeros 2, 3, -3, and 7-i.  Find the fifth zero and then determine g(x).\r<BR>\n" );
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document.write( "I understand the coefficients and know the 5th zero would have to be 7+i.  However, I'm not sure how to then determine g(x).  Can anyone help me?\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31010 by </B><A HREF=/tutors/aboutme.mpl?userid=adamchapman><B>adamchapman(301)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=adamchapman><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=31010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To have all real coefficients, any complex root (7-i) must have a corresponding conjugate root, (7+i) in this case.<BR>\n" );
document.write( "We Now know all the roots (values of x when g(x)=0:<BR>\n" );
document.write( "2, 3, -3, 7-i and 7+i<BR>\n" );
document.write( "So:<BR>\n" );
document.write( "g(x)=(x-2)(x-3)(x+3)(x-7+i)(x-7-i)\r<BR>\n" );
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document.write( "I hope this helps,<BR>\n" );
document.write( "Adam<BR>\n" );
document.write( "P.S. please visit my website, it may be helpful to you. The address is www.geocities.com/quibowibbler<BR>\n" );
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