document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160754>Question 1160754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Check that (2+i) is a root of z^4+2(z^3)-9(z^2)-10z+50=0. Find the remaining three roots. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784150 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=784150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E4%2B2z%5E3-9z%5E2-10z%2B50=0 ALIGN=MIDDLE  ALT=\"z%5E4%2B2z%5E3-9z%5E2-10z%2B50=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E4%2B+6z%5E3+%2B10z%5E2+-4z%5E3-24z%5E2-40z+%2B5z%5E2%2B30z+%2B50=0 ALIGN=MIDDLE  ALT=\"z%5E4%2B+6z%5E3+%2B10z%5E2+-4z%5E3-24z%5E2-40z+%2B5z%5E2%2B30z+%2B50=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%5E4-4z%5E3%2B5z%5E2%29%2B+%286z%5E3-24z%5E2%2B30z%29%2B%2810z%5E2-40z+%2B50%29=0 ALIGN=MIDDLE  ALT=\"%28z%5E4-4z%5E3%2B5z%5E2%29%2B+%286z%5E3-24z%5E2%2B30z%29%2B%2810z%5E2-40z+%2B50%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2%28z%5E2-4z%2B5%29%2B+6z%28z%5E2-4z%2B5%29%2B10%28z%5E2-4z+%2B5%29=0 ALIGN=MIDDLE  ALT=\"z%5E2%28z%5E2-4z%2B5%29%2B+6z%28z%5E2-4z%2B5%29%2B10%28z%5E2-4z+%2B5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%5E2+-+4+z+%2B+5%29+%28z%5E2+%2B+6+z+%2B+10%29+=+0 ALIGN=MIDDLE  ALT=\"%28z%5E2+-+4+z+%2B+5%29+%28z%5E2+%2B+6+z+%2B+10%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use quadratic function to find roots\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%5E2+-+4+z+%2B+5%29=0 ALIGN=MIDDLE  ALT=\"%28z%5E2+-+4+z+%2B+5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28-%28-4%29%2B-sqrt%28%28-4%29%5E2-4%2A1%2A5%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"z=%28-%28-4%29%2B-sqrt%28%28-4%29%5E2-4%2A1%2A5%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%284%2B-sqrt%2816-20%29%29%2F2 ALIGN=MIDDLE  ALT=\"z=%284%2B-sqrt%2816-20%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%284%2B-sqrt%28-4%29%29%2F2 ALIGN=MIDDLE  ALT=\"z=%284%2B-sqrt%28-4%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%284%2B-2i%29%2F2 ALIGN=MIDDLE  ALT=\"z=%284%2B-2i%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%282%2B-i%29 ALIGN=MIDDLE  ALT=\"z=%282%2B-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots are: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2%2Bi ALIGN=MIDDLE  ALT=\"z=2%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > ->is a root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E4%2B2z%5E3-9z%5E2-10z%2B50=0 ALIGN=MIDDLE  ALT=\"z%5E4%2B2z%5E3-9z%5E2-10z%2B50=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since complex roots always come in pairs, you also have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2-i ALIGN=MIDDLE  ALT=\"z=2-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and remaining roots are:\r<BR>\n" );
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document.write( " for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28z%5E2+%2B+6+z+%2B+10%29+=+0 ALIGN=MIDDLE  ALT=\"+%28z%5E2+%2B+6+z+%2B+10%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28-6%2B-sqrt%286%5E2-4%2A1%2A10%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"z=%28-6%2B-sqrt%286%5E2-4%2A1%2A10%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28-6%2B-sqrt%2836-40%29%29%2F2 ALIGN=MIDDLE  ALT=\"z=%28-6%2B-sqrt%2836-40%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28-6%2B-sqrt%28-4%29%29%2F2 ALIGN=MIDDLE  ALT=\"z=%28-6%2B-sqrt%28-4%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28-6%2B-2i%29%2F2 ALIGN=MIDDLE  ALT=\"z=%28-6%2B-2i%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28-3%2B-i%29 ALIGN=MIDDLE  ALT=\"z=%28-3%2B-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots are: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-3%2Bi ALIGN=MIDDLE  ALT=\"z=-3%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-3-i ALIGN=MIDDLE  ALT=\"z=-3-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );