document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003853>Question 1003853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you write a polynomial function of least degree with integral coefficients with these given zeros<BR>\n" );
document.write( "-1,-2+2i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620466 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=620466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "given zeros:<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;\" >,real zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-2%2B2i ALIGN=MIDDLE  ALT=\"x%5B2%5D=-2%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, complex zero\r<BR>\n" );
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document.write( "recall, complex zeros always coming in pairs; so, this function also have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=-2-2i ALIGN=MIDDLE  ALT=\"x%5B3%5D=-2-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a zero\r<BR>\n" );
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document.write( "now, use zero product theorem to find a function that has these three zeros\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29 ALIGN=MIDDLE  ALT=\"f%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=f%28x%29=%28x-%28-1%29%29%28x-%28-2%2B2i%29%29%28x-%28-2-2i%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-%28-1%29%29%28x-%28-2%2B2i%29%29%28x-%28-2-2i%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=f%28x%29=%28x%2B1%29%28x%2B2-2i%29%28x%2B2%2B2i%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B1%29%28x%2B2-2i%29%28x%2B2%2B2i%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=f%28x%29=%28x%2B1%29%28x%5E2%2B2x%2Bcross%282xi%29%2B2x%2B4%2Bcross%284i%29-cross%282xi%29-cross%284i%29-4i%5E2%29 ALIGN=MIDDLE   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=f%28x%29=%28x%2B1%29%28x%5E2%2B4x%2B4-4%28-1%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B1%29%28x%5E2%2B4x%2B4-4%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=f%28x%29=%28x%2B1%29%28x%5E2%2B4x%2B4%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B1%29%28x%5E2%2B4x%2B4%2B4%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=f%28x%29=%28x%2B1%29%28x%5E2%2B4x%2B8%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B1%29%28x%5E2%2B4x%2B8%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=f%28x%29=x%5E3%2B4x%5E2%2B8x%2Bx%5E2%2B4x%2B8 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B4x%5E2%2B8x%2Bx%5E2%2B4x%2B8\"   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=f%28x%29=x%5E3%2B5x%5E2%2B12x%2B8 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B5x%5E2%2B12x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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