document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005610>Question 1005610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a polynomial with rational coefficients so that P(x)=0 has the given roots: -1 and -2i? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621787 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=0 ALIGN=MIDDLE  ALT=\"P%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > has the given roots: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-2i ALIGN=MIDDLE  ALT=\"x%5B2%5D=-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-2i ALIGN=MIDDLE  ALT=\"x%5B2%5D=-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > then we also have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=2i ALIGN=MIDDLE  ALT=\"x%5B3%5D=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > because complex roots always come in pairs\r<BR>\n" );
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document.write( "use zero product formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28x-%28-1%29%29%28x-%28-2i%29%29%28x-2i%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28x-%28-1%29%29%28x-%28-2i%29%29%28x-2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28x%2B1%29%28x%2B2i%29%28x-2i%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28x%2B1%29%28x%2B2i%29%28x-2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28x%2B1%29%28x%5E2-%282i%29%5E2%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28x%2B1%29%28x%5E2-%282i%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28x%2B1%29%28x%5E2-4i%5E2%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28x%2B1%29%28x%5E2-4i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28x%2B1%29%28x%5E2-4%28-1%29%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28x%2B1%29%28x%5E2-4%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28x%2B1%29%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28x%2B1%29%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=x%5E3%2B4x%2Bx%5E2%2B4 ALIGN=MIDDLE  ALT=\"P%28x%29=x%5E3%2B4x%2Bx%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P%28x%29=x%5E3%2Bx%5E2%2B4x%2B4%29 ALIGN=MIDDLE  ALT=\"highlight%28P%28x%29=x%5E3%2Bx%5E2%2B4x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%2Bx%5E2%2B4x%2B4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%2Bx%5E2%2B4x%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );