document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074598>Question 1074598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an&#8203; nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing&#8203; utility, use it to graph the function and verify the real zeros and the given function value.\r<BR>\n" );
document.write( "\n" );
document.write( "n=3<BR>\n" );
document.write( "4 and 2i are zeroes<BR>\n" );
document.write( "f(1)=30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689250 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=689250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rational coefficients means that complex roots come in complex conjugate pairs.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-4%29%28x-2i%29%28x%2B2i%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-4%29%28x-2i%29%28x%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-4%29%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-4%29%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=a%281-4%29%281%5E2%2B4%29=30 ALIGN=MIDDLE  ALT=\"f%281%29=a%281-4%29%281%5E2%2B4%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28-3%29%285%29=30 ALIGN=MIDDLE  ALT=\"a%28-3%29%285%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15a=30 ALIGN=MIDDLE  ALT=\"-15a=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-2%28x-4%29%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-2%28x-4%29%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-2x%5E3%2B8x%5E2-8x%2B32 ALIGN=MIDDLE  ALT=\"f%28x%29=-2x%5E3%2B8x%5E2-8x%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );