document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010025>Question 1010025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation of the polynomial with a leading coefficient of 2, and with the roots: -6 6 and 2i? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625524 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=625524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "the polynomial with a leading coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and with the roots:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+-6 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=++6+ ALIGN=MIDDLE  ALT=\"x%5B2%5D=++6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=+2i ALIGN=MIDDLE  ALT=\"x%5B3%5D=+2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> if we have this root, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=+-2i ALIGN=MIDDLE  ALT=\"x%5B4%5D=+-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > because complex roots always come in pairs\r<BR>\n" );
document.write( "\n" );
document.write( "use zero product theorem  and a leading coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=2%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=2%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=2%28x-%28-6%29%29%28x-6%29%28x-2i%29%28x-%28-2i%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x-%28-6%29%29%28x-6%29%28x-2i%29%28x-%28-2i%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=2%28x%2B6%29%28x-6%29%28x-2i%29%28x%2B2i%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%2B6%29%28x-6%29%28x-2i%29%28x%2B2i%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=2%28x%5E2-6%5E2%29%28x%5E2-%282i%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%5E2-6%5E2%29%28x%5E2-%282i%29%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=2%28x%5E2-36%29%28x%5E2-4i%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%5E2-36%29%28x%5E2-4i%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=2%28x%5E2-36%29%28x%5E2-4%28-1%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%5E2-36%29%28x%5E2-4%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=2%28x%5E2-36%29%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%5E2-36%29%28x%5E2%2B4%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=2%28x%5E4-32x%5E2-144%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%5E4-32x%5E2-144%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=2x%5E4-64x%5E2-288 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E4-64x%5E2-288\"   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" );