document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126935>Question 1126935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Form a&#8203; fifth-degree polynomial function with real coefficients such that 2i,1-2i, and -5 are zeros and f(0)=200. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743275 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=743275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "given: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=2i ALIGN=MIDDLE  ALT=\"x%5B1%5D=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, if that zero given,  the conjugate  <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;\" > must also be a zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=1-2i ALIGN=MIDDLE  ALT=\"x%5B3%5D=1-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  we  also have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=1%2B2i ALIGN=MIDDLE  ALT=\"x%5B4%5D=1%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "recall: complex zeros always come in pairs\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B5%5D=+-5+ ALIGN=MIDDLE  ALT=\"x%5B5%5D=+-5+\"   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%280%29=200 ALIGN=MIDDLE  ALT=\"+f%280%29=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=C%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29%28x-x%5B5%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29%28x-x%5B5%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a constant, we put this for the y-intercept condition\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=C%28x-2i%29%28x-%28-2i%29%29%28x-%281-2i%29%29%28x-%281%2B2i%29%29%28x-%28-5%29%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x-2i%29%28x-%28-2i%29%29%28x-%281-2i%29%29%28x-%281%2B2i%29%29%28x-%28-5%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=C%28x-2i%29%28x%2B2i%29%28x-1%2B2i%29%28x-1-2i%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x-2i%29%28x%2B2i%29%28x-1%2B2i%29%28x-1-2i%29%28x%2B5%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=C%28x%5E2-4i%5E2%29%28x%5E2+-+2+x+%2B+5%29%28x%2B5%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x%5E2-4i%5E2%29%28x%5E2+-+2+x+%2B+5%29%28x%2B5%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=C%28x%5E2-4%28-1%29%29%28x%5E3+%2B+3+x%5E2+-+5+x+%2B+25%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x%5E2-4%28-1%29%29%28x%5E3+%2B+3+x%5E2+-+5+x+%2B+25%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=C%28x%5E2%2B4%29%28x%5E3+%2B+3+x%5E2+-+5+x+%2B+25%29 ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x%5E2%2B4%29%28x%5E3+%2B+3+x%5E2+-+5+x+%2B+25%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=C%28x%5E5+%2B+3+x%5E4+-+x%5E3+%2B+37+x%5E2+-+20+x+%2B+100+%29 ALIGN=MIDDLE  ALT=\"f%28x%29=C%28x%5E5+%2B+3+x%5E4+-+x%5E3+%2B+37+x%5E2+-+20+x+%2B+100+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the fact that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=200 ALIGN=MIDDLE  ALT=\"f%280%29=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200+=+C+%280%5E5+%2B+3+%2A0%5E4+-+0%5E3+%2B+37%2A0%5E2+-+20+%2A0+%2B+100+%29 ALIGN=MIDDLE  ALT=\"200+=+C+%280%5E5+%2B+3+%2A0%5E4+-+0%5E3+%2B+37%2A0%5E2+-+20+%2A0+%2B+100+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200+=+100C ALIGN=MIDDLE  ALT=\"200+=+100C\"   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=C=200%2F100 ALIGN=MIDDLE  ALT=\"C=200%2F100\"   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=C=2 ALIGN=MIDDLE  ALT=\"C=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%28x%5E5+%2B+3+x%5E4+-+x%5E3+%2B+37+x%5E2+-+20+x+%2B+100+%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%5E5+%2B+3+x%5E4+-+x%5E3+%2B+37+x%5E2+-+20+x+%2B+100+%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=f%28x%29=2x%5E5+%2B+6x%5E4+-+2x%5E3+%2B+74x%5E2+-+40+x+%2B+200+ ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E5+%2B+6x%5E4+-+2x%5E3+%2B+74x%5E2+-+40+x+%2B+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );