document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099340>Question 1099340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me with this question - Thanks<BR>\n" );
document.write( "Let P(z)= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z%5E3-kz%5E2%2B22z-20+ ALIGN=MIDDLE  ALT=\"+z%5E3-kz%5E2%2B22z-20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , k is a rational number. <BR>\n" );
document.write( "3+i is a root of the equation P(z)=0<BR>\n" );
document.write( "Find value of k.<BR>\n" );
document.write( "Find the other root of the equation P(z)=0\r<BR>\n" );
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document.write( "I got two roots and multiplied them together and got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z%5E2-6z%2B10+ ALIGN=MIDDLE  ALT=\"+z%5E2-6z%2B10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, I did this by z=3+i and z=3-i, (z-3-i)(z-3+i).<BR>\n" );
document.write( "I originally thought I had to divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z%5E3-kz%5E2%2B22z-20+ ALIGN=MIDDLE  ALT=\"+z%5E3-kz%5E2%2B22z-20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z%5E2-6z%2B10+ ALIGN=MIDDLE  ALT=\"+z%5E2-6z%2B10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > but I don't think I can divide with the k in the way.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713790 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z%29=%28z%5E2-6z%2B10%29%28z-r%29 ALIGN=MIDDLE  ALT=\"P%28z%29=%28z%5E2-6z%2B10%29%28z-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the other root.<BR>\n" );
document.write( "The independent term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10r=-20 ALIGN=MIDDLE  ALT=\"-10r=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2 ALIGN=MIDDLE  ALT=\"r=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or we were deceived about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Bi ALIGN=MIDDLE  ALT=\"3%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > being a root.<BR>\n" );
document.write( "Let's multiply.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z%29=%28z%5E2-6z%2B10%29%28z-2%29=z%5E3-6z%5E2%2B10z-2z%5E2%2B12z-20=z%5E3-8z%5E2%2B22z-20 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If that polynomial is the same function as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z%29=z%5E3-kz%5E2%2B22z-20+ ALIGN=MIDDLE  ALT=\"P%28z%29=z%5E3-kz%5E2%2B22z-20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(same values for every complex value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > ),<BR>\n" );
document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=8 ALIGN=MIDDLE  ALT=\"k=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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