document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200976>Question 1200976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an nth degree polynomial function with real coefficients, a leading coefficient of 1 and satisfying the given conditions n=3   -5 and 2+5i are zeros </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835193 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If the coefficients of the polynomial are real and 2+5i is a root, then 2-5i is also a root.<br><BR>\n" );
document.write( "So the three roots are<BR>\n" );
document.write( "-5<BR>\n" );
document.write( "2+5i<BR>\n" );
document.write( "2-5i<br><BR>\n" );
document.write( "and the polynomial is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-%28-5%29%29%28x-%282%2B5i%29%29%28x-%282-5i%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-%28-5%29%29%28x-%282%2B5i%29%29%28x-%282-5i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where a can be any constant.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-5%29%29=%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28x-%28-5%29%29=%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%282%2B5i%29%29%28x-%282-5i%29%29=%28%28x-2%29-5i%29%28%28x-2%29%2B5i%29=%28x%5E2-4x%2B4%29-25i%5E2=%28x%5E2-4x%2B4%29%2B25=x%5E2-4x%2B29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%28x%5E2-4x%2B29%29=x%5E3-4x%5E2%2B29x%2B5x%5E2-20x%2B145=x%5E3%2Bx%5E2%2B9x%2B145 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x%5E3%2Bx%5E2%2B9x%2B145%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x%5E3%2Bx%5E2%2B9x%2B145%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );