document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=493151>Question 493151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find a polynomial function with rational coefficients so that P(x)=0 has the given roots: 13i and 5 + 10i.\r<BR>\n" );
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document.write( "I tried this: <BR>\n" );
document.write( "P(x)=(x+13i)(x^2 + 5 + 10) but when I multiply everything out it is Way off from the answer in the back of the book.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335308 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=335308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> complex roots (those containing i) occur in conjugate pairs (a+bi and a-bi)<BR>\n" );
document.write( "___ also; if r is a root, then x-r is a factor\r<BR>\n" );
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document.write( "so P(x) has four factors ___ (x + 13i)(x - 13i)[x - (5 + 10i)][x - (5 - 10i)]\r<BR>\n" );
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document.write( "multiplying the factors should give you the right result </SPAN>\n" );
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