document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=709832>Question 709832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write a polynomial function with rational coefficients so that it has roots         (-2, 1+3i ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436799 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=436799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You seem to be asking for polynomial function with roots: -2,and  1+3i, AND 1-3i.  Complex roots come as conjugate pairs.\r<BR>\n" );
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document.write( "-2 is a root:<BR>\n" );
document.write( "((-2)-(k))=0<BR>\n" );
document.write( "-2-k=0<BR>\n" );
document.write( "-k=2<BR>\n" );
document.write( "k=-2<BR>\n" );
document.write( "The binomial factor is (x-(-2))=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1+3i is a root:<BR>\n" );
document.write( "(1+3i-k)=0<BR>\n" );
document.write( "1+3i-k=0<BR>\n" );
document.write( "-k=-1-3i<BR>\n" );
document.write( "The binomial factor is (x-(-1-3i))<BR>\n" );
document.write( "or equal to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B%281%2B3i%29%29 ALIGN=MIDDLE  ALT=\"+%28x%2B%281%2B3i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1-3i is a root:<BR>\n" );
document.write( "(1-3i-k)=0<BR>\n" );
document.write( "-k=-1+3i<BR>\n" );
document.write( "k=1-3i<BR>\n" );
document.write( "The binomial factor is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%281-3i%29%29 ALIGN=MIDDLE  ALT=\"%28x-%281-3i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A satisfying function can come from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x%2B%281%2B3i%29%29%28x-%281-3i%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x%2B%281%2B3i%29%29%28x-%281-3i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Do the multiplications, at least for the factors containing the complex numbers:<BR>\n" );
document.write( "... The finished polynomial function may be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=%28x%2B2%29%28x%5E2-2x%2B10%29%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=%28x%2B2%29%28x%5E2-2x%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you could do the rest of the multiplying if needed. </SPAN>\n" );
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