document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191999>Question 1191999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Form a fifth-degree polynomial function with real coefficients such that 5i, 1-3i, and -3 are zeros and f(0)=1500 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823874 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> complex roots are conjugate<BR>\n" );
document.write( "roots are +/-5i<BR>\n" );
document.write( "1-3i, 1+3i<BR>\n" );
document.write( "-3<BR>\n" );
document.write( "Two factors are (x^2+25)(x+3)<BR>\n" );
document.write( "The other two are (x+1+3i) (x-1-3i)<BR>\n" );
document.write( "multiply those to get x^2-2x+10, which has roots (1/2)(2+/-sqrt(-36)) or (1/2) (2+/-6i)<BR>\n" );
document.write( "=x^2-2x+10<BR>\n" );
document.write( "a(x^2+25)(x+3)(x^2-2x+10) is the polynomial<BR>\n" );
document.write( "when x=0 the value is 25*3*10=750, so a must be 2.<BR>\n" );
document.write( "2(x^2+25)(x+3)(x^2-2x+10)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-200%2C2000%2C2%28x%5E2%2B25%29%28x%2B3%29%28x%5E2-2x%2B10%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );