document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006537>Question 1006537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) Thanks!\r<BR>\n" );
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document.write( "6, 7 + i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622658 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52797)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=622658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "p(x) = (x-6)*(x-(7+i))*(x-(7-i)) = (x-6)*(x^2 - 14x + 50).\r<BR>\n" );
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document.write( "It is based on two theorems.\r<BR>\n" );
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document.write( "First theorem says: <BR>\n" );
document.write( "\"If a polynomial with real coefficients has a complex root (the root which is complex number) \r<BR>\n" );
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document.write( "then it has the root which is complex conjugate to the first one\".\r<BR>\n" );
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document.write( "Second theorem says: <BR>\n" );
document.write( "\"If a polynomial p(x) of degree n with the leading coefficient 1 at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5En ALIGN=MIDDLE  ALT=\"x%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > has n roots <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, . . . , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bn%5D ALIGN=MIDDLE  ALT=\"x%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "then the polynomial is p(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"%28x+-+x%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >* . . . *<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-x%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"%28x-x%5Bn%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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