document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763112>Question 763112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the nth-degree polynomial function with real coefficients satisfying the given conditions. <BR>\n" );
document.write( "n=4; i and 5i are zeros; f(-1)=52\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464504 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=464504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "You are given three roots: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5i ALIGN=MIDDLE  ALT=\"5i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a root, so must its conjugate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i ALIGN=MIDDLE  ALT=\"-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > also be a root,  <BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5i ALIGN=MIDDLE  ALT=\"5i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a root, so must its conjugate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5i ALIGN=MIDDLE  ALT=\"-5i\"   DISABLED_style= \"max-width:90%; height:auto;\" > also be a root\r<BR>\n" );
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document.write( "You can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by using zero product rule \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%2Bi%29%28x-i%29%28x%2B5i%29%28x-5i%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2Bi%29%28x-i%29%28x%2B5i%29%28x-5i%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%5E2-i%5E2%29%28x%5E2-%285i%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2-i%5E2%29%28x%5E2-%285i%29%5E2%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%5E2-%28-1%29%29%28x%5E2-25i%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2-%28-1%29%29%28x%5E2-25i%5E2%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%5E2%2B1%29%28x%5E2-25%28-1%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B1%29%28x%5E2-25%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%5E2%2B1%29%28x%5E2%2B25%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B1%29%28x%5E2%2B25%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%5E4%2B25x%5E2%2Bx%5E2%2B25 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4%2B25x%5E2%2Bx%5E2%2B25\"   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%5E4%2B26x%5E2%2B25 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4%2B26x%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" >....your polynomial\r<BR>\n" );
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document.write( "check if<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=52 ALIGN=MIDDLE  ALT=\"f%28-1%29=52\"   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%28-1%29=%28-1%29%5E4%2B26%28-1%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"f%28-1%29=%28-1%29%5E4%2B26%28-1%29%5E2%2B25\"   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%28-1%29=1%2B26%2A1%2B25 ALIGN=MIDDLE  ALT=\"f%28-1%29=1%2B26%2A1%2B25\"   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%28-1%29=52 ALIGN=MIDDLE  ALT=\"f%28-1%29=52\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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