document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475872>Question 475872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation x&#8308;-2x²-16x-15 has four roots.  If two of the roots are real and equal to x=-1 and x=3, by a process of long division and solving a quadratic equation find the two complex roots </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326414 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=326414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-1+ ALIGN=MIDDLE  ALT=\"+x+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+x+%2B+1+=+0+\"   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+=+3+ ALIGN=MIDDLE  ALT=\"+x+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+3+=+0+ ALIGN=MIDDLE  ALT=\"+x+-+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Complex roots come in pairs<BR>\n" );
document.write( "of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+bi+ ALIGN=MIDDLE  ALT=\"+a+%2B+bi+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+-+bi+ ALIGN=MIDDLE  ALT=\"+a+-+bi+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+1%29%2A%28x+-+3%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+1%29%2A%28x+-+3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+1%29%2A%28x+-+3%29+=+x%5E2+-+2x+-+3+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+1%29%2A%28x+-+3%29+=+x%5E2+-+2x+-+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E4+-+2x%5E2+-+16x+-+15%29+%2F+%28x%5E2+-+2x+-+3%29+=+x%5E2+%2B+2x+%2B+5+ ALIGN=MIDDLE  ALT=\"+%28x%5E4+-+2x%5E2+-+16x+-+15%29+%2F+%28x%5E2+-+2x+-+3%29+=+x%5E2+%2B+2x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can use quadratic formula now<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+2+ ALIGN=MIDDLE  ALT=\"+b+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+5+ ALIGN=MIDDLE  ALT=\"+c+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+4+-+20+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+4+-+20+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+-16+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+-16+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B+4i%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B+4i%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-1+%2B+2i+ ALIGN=MIDDLE  ALT=\"+x+=+-1+%2B+2i+\"   DISABLED_style= \"max-width:90%; height:auto;\" > 1st root <BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+-+4i%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+-+4i%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-1+-+2i+ ALIGN=MIDDLE  ALT=\"+x+=+-1+-+2i+\"   DISABLED_style= \"max-width:90%; height:auto;\" > 2nd root\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );