document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129188>Question 1129188</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( "-3 and 3+5i are zeros;<BR>\n" );
document.write( "f (1) = 116\r<BR>\n" );
document.write( "\n" );
document.write( "f(x)= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745768 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</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=745768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The non-real zeros come in conjugate pairs; so the 3 roots are -3, 3+5i,and 3-5i.  Then the polynomial is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-%28-3%29%29%28x-%283%2B5i%29%29%28x-%283-5i%29%29 ALIGN=MIDDLE  ALT=\"a%28x-%28-3%29%29%28x-%283%2B5i%29%29%28x-%283-5i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%2B3%29%28%28x-3%29-5i%29%28%28x-3%29%2B5i%29 ALIGN=MIDDLE  ALT=\"a%28x%2B3%29%28%28x-3%29-5i%29%28%28x-3%29%2B5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%2B3%29%28%28x%5E2-6x%2B9%29%2B25%29 ALIGN=MIDDLE  ALT=\"a%28x%2B3%29%28%28x%5E2-6x%2B9%29%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%2B3%29%28x%5E2-6x%2B34%29 ALIGN=MIDDLE  ALT=\"a%28x%2B3%29%28x%5E2-6x%2B34%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To determine the value of the leading coefficient a, use the given fact that f(1)=116:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%284%29%2829%29+=+116a+=+116 ALIGN=MIDDLE  ALT=\"a%284%29%2829%29+=+116a+=+116\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1 ALIGN=MIDDLE  ALT=\"a+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the leading coefficient is 1, and the polynomial is found by performing the indicated multiplication.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x%2B3%29%28x%5E2-6x%2B34%29+=+x%5E3-3x%5E2%2B16x%2B102 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x%2B3%29%28x%5E2-6x%2B34%29+=+x%5E3-3x%5E2%2B16x%2B102\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );