document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1000695>Question 1000695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5+i and 1+4i<BR>\n" );
document.write( "Find a polynomial function f(x) of least degree having only real coefficients with zeros as given </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618040 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=618040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=5%2Bi ALIGN=MIDDLE  ALT=\"x%5B1%5D=5%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=1%2B4i ALIGN=MIDDLE  ALT=\"x%5B2%5D=1%2B4i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since given zeros are complex solutions, they always come in pairs<BR>\n" );
document.write( "have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=5-i ALIGN=MIDDLE  ALT=\"x%5B3%5D=5-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=1-4i ALIGN=MIDDLE  ALT=\"x%5B4%5D=1-4i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%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-%285%2Bi%29%29%28x-%281%2B4i%29%29%28x-%285-i%29%29%28x-%281-4i%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-%285%2Bi%29%29%28x-%281%2B4i%29%29%28x-%285-i%29%29%28x-%281-4i%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-5-i%29%28x-1-4i%29%28x-5%2Bi%29%28x-1%2B4i%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-5-i%29%28x-1-4i%29%28x-5%2Bi%29%28x-1%2B4i%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%2B%28-6-5i%29x%2B21i%2B1%29%28x%5E2%2B%28-6%2B5i%29x-21i%2B1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B%28-6-5i%29x%2B21i%2B1%29%28x%5E2%2B%28-6%2B5i%29x-21i%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...multiplying each term by each, and knowing that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Ai=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%2Ai=i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 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=x%5E4-12x%5E3%2B63x%5E2-222x%2B442 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-12x%5E3%2B63x%5E2-222x%2B442\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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