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 #689254 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=689254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "If 2i is a zero, then -2i is also.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "--> (x-4)*(x-2i)*(x+2i) = 0<BR>\n" );
document.write( "(x-4)*(x^2+4) = 0<BR>\n" );
document.write( "f(x) = x^3 - 4x^2 + 4x - 16<BR>\n" );
document.write( "----<BR>\n" );
document.write( "f(1) = 1 - 4 + 4 - 16 = -15<BR>\n" );
document.write( "Multiply by -2<BR>\n" );
document.write( "--> f(x) = -2x^3 + 8x^2 - 8x + 32<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );