document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129075>Question 1129075</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.\r<BR>\n" );
document.write( "\n" );
document.write( "3, -13, and 5 + 4i  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745623 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=745623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "given roots:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=3 ALIGN=MIDDLE  ALT=\"x%5B1%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=+-13 ALIGN=MIDDLE  ALT=\"x%5B2%5D=+-13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=5+%2B+4i ALIGN=MIDDLE  ALT=\"x%5B3%5D=5+%2B+4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > => recall that complex roots always come in pairs; so, you will also have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=5-+4i ALIGN=MIDDLE  ALT=\"x%5B4%5D=5-+4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-3%29%28x-%28-13%29%29%28x-%285+%2B+4i%29%29%28x-%285-+4i%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-3%29%28x-%28-13%29%29%28x-%285+%2B+4i%29%29%28x-%285-+4i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-3%29%28x%2B13%29%28x-5+-+4i%29%28x-5%2B+4i%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-3%29%28x%2B13%29%28x-5+-+4i%29%28x-5%2B+4i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2B13x-3x-39%29%28x%5E2-5x%2B+4xi-5x%2B25-20i-4xi%2B20i-16i%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B13x-3x-39%29%28x%5E2-5x%2B+4xi-5x%2B25-20i-4xi%2B20i-16i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B25-16%28-1%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B25-16%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B25%2B16%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B25%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B41%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B41%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4+-+98x%5E2+%2B+800x+-+1599 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4+-+98x%5E2+%2B+800x+-+1599\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );