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 #464507 by </B><A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><B>tommyt3rd(5050)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><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=tommyt3rd><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=464507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since coefficients are real this must mean that the complex roots occur in conjugate pairs. We can write:\r<BR>\n" );
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document.write( "and given that f(-1)=52 we can determine a...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28%28-1%29%5E2%2B1%5E2%29%28%28-1%29%5E2%2B5%5E2%29=52 ALIGN=MIDDLE  ALT=\"a%28%28-1%29%5E2%2B1%5E2%29%28%28-1%29%5E2%2B5%5E2%29=52\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so that\r<BR>\n" );
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document.write( "and a=1\r<BR>\n" );
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document.write( "this leads to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Af%28x%29=%28x%5E2%2B1%29%28x%5E2%2B25%29=x%5E4%2B26x%5E2%2B25%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Af%28x%29=%28x%5E2%2B1%29%28x%5E2%2B25%29=x%5E4%2B26x%5E2%2B25%0D%0A\"   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%0D%0A ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4%2B26x%5E2%2B25%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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