document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=745890>Question 745890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a polynomial function with rational coefficients so that P(x)=0 has the given roots.<BR>\n" );
document.write( "1.) -4 and 5i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454050 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=454050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> complex roots of polynomials with real always come in conjugate pairs so if 5i is a root, then so is -5i.\r<BR>\n" );
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document.write( "so the general polynomial is...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=Q%28x%29%28x-4%29%28x-5i%29%28x%2B5i%29 ALIGN=MIDDLE  ALT=\"p=Q%28x%29%28x-4%29%28x-5i%29%28x%2B5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "but the principal polynomial is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%28x-4%29%28x-5i%29%28x%2B5i%29 ALIGN=MIDDLE  ALT=\"p=%28x-4%29%28x-5i%29%28x%2B5i%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=%28x-4%29%28x%5E2%2B25%29 ALIGN=MIDDLE  ALT=\"%28x-4%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=x%28x%5E2%2B25%29-4%28x%5E2%2B25%29 ALIGN=MIDDLE  ALT=\"x%28x%5E2%2B25%29-4%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=x%5E3%2B25x-4x%5E2-100%29 ALIGN=MIDDLE  ALT=\"x%5E3%2B25x-4x%5E2-100%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=x%5E3-4x%5E2%2B25x-100%29 ALIGN=MIDDLE  ALT=\"x%5E3-4x%5E2%2B25x-100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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