document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161068>Question 1161068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation for p p is a degree 5 polynomial that passes through the origin, has zeros i and 4−i, and p(5)=520 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784491 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=784491\">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=p%28x%29 ALIGN=MIDDLE  ALT=\"p%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a degree<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5 ALIGN=MIDDLE  ALT=\"+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "has zeros :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=i+ ALIGN=MIDDLE  ALT=\"x%5B1%5D=i+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> complex zeros always come in pair, so you also have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-i+ ALIGN=MIDDLE  ALT=\"x%5B2%5D=-i+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=4-i+ ALIGN=MIDDLE  ALT=\"x%5B3%5D=4-i+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and also<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=4%2Bi+ ALIGN=MIDDLE  ALT=\"x%5B4%5D=4%2Bi+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "passes through the origin: point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)-> 5th root is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B5%5D=0 ALIGN=MIDDLE  ALT=\"x%5B5%5D=0\"   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%285%29=520 ALIGN=MIDDLE  ALT=\"p%285%29=520\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use zero product rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=a%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=\"p%28x%29=a%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;\" >....substitute given zeros\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=p%28x%29=a%28x-i%29%28x-%28-i%29%29%28x-%284-i+%29%29%28x-%284%2Bi+%29%29%28x-0%29 ALIGN=MIDDLE  ALT=\"p%28x%29=a%28x-i%29%28x-%28-i%29%29%28x-%284-i+%29%29%28x-%284%2Bi+%29%29%28x-0%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=a%28x%5E5+-+8x%5E4+%2B+18x%5E3+-+8x%5E2+%2B+17x%29 ALIGN=MIDDLE  ALT=\"p%28x%29=a%28x%5E5+-+8x%5E4+%2B+18x%5E3+-+8x%5E2+%2B+17x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......since we are given<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%285%29=520 ALIGN=MIDDLE  ALT=\"p%285%29=520\"   DISABLED_style= \"max-width:90%; height:auto;\" >, use it to find   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   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=520=a%285%5E5+-+8%2A5%5E4+%2B+18%2A5%5E3+-+8%2A5%5E2+%2B+17%2A5%29 ALIGN=MIDDLE  ALT=\"520=a%285%5E5+-+8%2A5%5E4+%2B+18%2A5%5E3+-+8%2A5%5E2+%2B+17%2A5%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=520=a%28260%29 ALIGN=MIDDLE  ALT=\"520=a%28260%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=a=520%2F260 ALIGN=MIDDLE  ALT=\"a=520%2F260\"   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=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and your equation is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=2%28x%5E5+-+8x%5E4+%2B+18x%5E3+-+8x%5E2+%2B+17x%29 ALIGN=MIDDLE  ALT=\"p%28x%29=2%28x%5E5+-+8x%5E4+%2B+18x%5E3+-+8x%5E2+%2B+17x%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=2x%5E5+-+16x%5E4+%2B+36x%5E3+-+16x%5E2+%2B+34x+ ALIGN=MIDDLE  ALT=\"p%28x%29=2x%5E5+-+16x%5E4+%2B+36x%5E3+-+16x%5E2+%2B+34x+\"   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+-5%2C+5%2C+-1000%2C+1000%2C+2x%5E5+-+16x%5E4+%2B+36x%5E3+-+16x%5E2+%2B+34x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );