document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263696>Question 263696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. <BR>\n" );
document.write( "P has degree 3, and zeros 1 and 4 + 4i.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194312 by </B><A HREF=/tutors/aboutme.mpl?userid=palanisamy><B>palanisamy(496)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=palanisamy><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given zeros are 1 and 4+4i<BR>\n" );
document.write( "We know that complex roots occur in conjugate pairs.<BR>\n" );
document.write( "Since 4+4i is one zero, 4-4i is also another zero.<BR>\n" );
document.write( "The required equation is<BR>\n" );
document.write( "         (x-1)[x-(4+4i][x-(4-4i)] = 0<BR>\n" );
document.write( "         (x-1)[(x-4)-4i][(x-4)+4i] = 0<BR>\n" );
document.write( "         (x-1)[(x-4)^2-(4i)^2]=0<BR>\n" );
document.write( "         (x-1)[x^2-8x+16+16] =0<BR>\n" );
document.write( "         (x-1){x^2-8x+32]=0<BR>\n" );
document.write( "          x^3-8x^2+32x-x^2+8x-32=0<BR>\n" );
document.write( "          x^3-9x^2+40x-32 = 0        </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );