document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065196>Question 1065196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to find polynomial with solutions: (0, 2-&#8730;3, 3) ? <BR>\n" );
document.write( "So far I did (x-0)(x+3i)(x-3i), but am not sure what to do for 2-&#8730;3. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680305 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</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=680305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The correct question is:\r<BR>\n" );
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document.write( "    How to find a polynomial with integer coefficients, having the roots 0, 2- sqrt(3) and 3 ?\r\n" );
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document.write( "Such a polynomial together with the root 2-sqrt(3), must have the root 2+sqrt(3), too.\r<BR>\n" );
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document.write( "So, the polynomial must have factors \r<BR>\n" );
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document.write( "     x                 for the root 0;\r\n" );
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document.write( "     (x-(2-sqrt(3)))   for the root  (2-sqrt(3));\r\n" );
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document.write( "     (x-(2+sqrt(3)))   for the root  (2+sqrt(3));\r\n" );
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document.write( "     (x-3)             for the root 3.\r\n" );
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document.write( "Thus the polynomial must be a multiple to \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp; p(x) = x*(x(x-(2-sqrt(3)))((x-(2+sqrt(3)))*(x-3)\r<BR>\n" );
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document.write( "You may write it in more convenient form.\r<BR>\n" );
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