document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=772758>Question 772758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If one of the roots of the quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%282k-5%29x%2Bk%5E2-5k%2B56%2F9=0 ALIGN=MIDDLE  ALT=\"x%5E2-%282k-5%29x%2Bk%5E2-5k%2B56%2F9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is twice the other,show that one of the roots is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k-5%29%2F3 ALIGN=MIDDLE  ALT=\"%282k-5%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.Hence find the values of the constant k.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471097 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=471097\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If one of the roots of the quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%282k-5%29x%2Bk%5E2-5k%2B56%2F9=0 ALIGN=MIDDLE  ALT=\"x%5E2-%282k-5%29x%2Bk%5E2-5k%2B56%2F9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is twice the other,show that one of the roots is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k-5%29%2F3 ALIGN=MIDDLE  ALT=\"%282k-5%29%2F3\"   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=%28%282k-5%29%2F3%29%282%28%282k-5%29%2F3%29%29=0 ALIGN=MIDDLE  ALT=\"%28%282k-5%29%2F3%29%282%28%282k-5%29%2F3%29%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=%282k-5%29%282%282k-5%29%29=0 ALIGN=MIDDLE  ALT=\"%282k-5%29%282%282k-5%29%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=%282k-5%29%284k-10%29=0 ALIGN=MIDDLE  ALT=\"%282k-5%29%284k-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=8k%5E2-20k-20k%2B50=0 ALIGN=MIDDLE  ALT=\"8k%5E2-20k-20k%2B50=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=8k%5E2-40k%2B50=0 ALIGN=MIDDLE  ALT=\"8k%5E2-40k%2B50=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=k+=+%28-%28-40%29+%2B-+sqrt%28+%28-40%29%5E2-4%2A8%2A50+%29%29%2F%282%2A8%29+ ALIGN=MIDDLE  ALT=\"k+=+%28-%28-40%29+%2B-+sqrt%28+%28-40%29%5E2-4%2A8%2A50+%29%29%2F%282%2A8%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=k+=+%2840+%2B-+sqrt%281600-1600+%29%29%2F16+ ALIGN=MIDDLE  ALT=\"k+=+%2840+%2B-+sqrt%281600-1600+%29%29%2F16+\"   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+=+%2840+%2B-+sqrt%280+%29%29%2F16+ ALIGN=MIDDLE  ALT=\"k+=+%2840+%2B-+sqrt%280+%29%29%2F16+\"   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+=+40+%2F16+ ALIGN=MIDDLE  ALT=\"k+=+40+%2F16+\"   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+=+5+%2F2+ ALIGN=MIDDLE  ALT=\"k+=+5+%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.... the values of the constant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, plug it in given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%282k-5%29x%2Bk%5E2-5k%2B56%2F9=0 ALIGN=MIDDLE  ALT=\"x%5E2-%282k-5%29x%2Bk%5E2-5k%2B56%2F9=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=x%5E2-%280%29x%2B%285%2F2%29%5E2-5%285%2F2%29%2B56%2F9=0 ALIGN=MIDDLE  ALT=\"x%5E2-%280%29x%2B%285%2F2%29%5E2-5%285%2F2%29%2B56%2F9=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=x%5E2%2B25%2F4-25%2F2%2B56%2F9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B25%2F4-25%2F2%2B56%2F9=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=x%5E2%2B25%2F4-50%2F4%2B56%2F9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B25%2F4-50%2F4%2B56%2F9=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=x%5E2-25%2F4%2B56%2F9=0 ALIGN=MIDDLE  ALT=\"x%5E2-25%2F4%2B56%2F9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2825%2A9%29%2F%284%2A9%29%2B%2856%2A4%29%2F%289%2A4%29=-225%2F36%2B216%2F36=-1%2F36 ALIGN=MIDDLE  ALT=\"-%2825%2A9%29%2F%284%2A9%29%2B%2856%2A4%29%2F%289%2A4%29=-225%2F36%2B216%2F36=-1%2F36\"   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=x%5E2-1%2F36=0 ALIGN=MIDDLE  ALT=\"x%5E2-1%2F36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k-5%29%2F3 ALIGN=MIDDLE  ALT=\"%282k-5%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%285+%2F2%29-5%29%2F3=%285-5%29%2F3=0 ALIGN=MIDDLE  ALT=\"%282%285+%2F2%29-5%29%2F3=%285-5%29%2F3=0\"   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=2%282k-5%29%2F3 ALIGN=MIDDLE  ALT=\"2%282k-5%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%282%285+%2F2%29-5%29%2F3=2%285-5%29%2F3=0 ALIGN=MIDDLE  ALT=\"2%282%285+%2F2%29-5%29%2F3=2%285-5%29%2F3=0\"   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=+graph%28600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-1%2F36%29+ ALIGN=MIDDLE  ALT=\"+graph%28600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-1%2F36%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );