document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050396>Question 1050396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that x=2 is a zero of f(x)=x^2+3kx+2k^2 (that is, f(2)=0). Find the value(s) of k.\r<BR>\n" );
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document.write( "Could you please show the steps and explain how you got there??\r<BR>\n" );
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document.write( "This is a question to help me better understand what I missed in class the other day; I have a quiz tomorrow! Please help!\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665959 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=665959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The idea is to plug in x = 2 and replace f(2) with 0. Then solve for k.\r<BR>\n" );
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document.write( "------------------------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B3kx%2B2k%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B3kx%2B2k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=%282%29%5E2%2B3k%2A%282%29%2B2k%5E2 ALIGN=MIDDLE  ALT=\"f%282%29=%282%29%5E2%2B3k%2A%282%29%2B2k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every x with 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=4%2B6k%2B2k%5E2 ALIGN=MIDDLE  ALT=\"f%282%29=4%2B6k%2B2k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4%2B6k%2B2k%5E2 ALIGN=MIDDLE  ALT=\"0=4%2B6k%2B2k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace the \"f(2)\" with 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2k%5E2%2B6k%2B4 ALIGN=MIDDLE  ALT=\"0=2k%5E2%2B6k%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k%5E2%2B6k%2B4=0 ALIGN=MIDDLE  ALT=\"2k%5E2%2B6k%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28k%5E2%2B3k%2B2%29=0 ALIGN=MIDDLE  ALT=\"2%28k%5E2%2B3k%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28k%5E2%2B3k%2B2%29%29%2F2=0%2F2 ALIGN=MIDDLE  ALT=\"%282%28k%5E2%2B3k%2B2%29%29%2F2=0%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%2B3k%2B2=0 ALIGN=MIDDLE  ALT=\"k%5E2%2B3k%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2B1%29%28k%2B2%29=0 ALIGN=MIDDLE  ALT=\"%28k%2B1%29%28k%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B1=0 ALIGN=MIDDLE  ALT=\"k%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B2=0 ALIGN=MIDDLE  ALT=\"k%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the zero product property. Then isolate k for each equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B1-1=0-1 ALIGN=MIDDLE  ALT=\"k%2B1-1=0-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B2-2=0-2 ALIGN=MIDDLE  ALT=\"k%2B2-2=0-2\"   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=k=-1 ALIGN=MIDDLE  ALT=\"k=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-2 ALIGN=MIDDLE  ALT=\"k=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "------------------------------------------------------------------------\r<BR>\n" );
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document.write( "So the values of k are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-1 ALIGN=MIDDLE  ALT=\"k=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-2 ALIGN=MIDDLE  ALT=\"k=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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