document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697245>Question 697245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kx^2+kx+5=0 what is the value of \"k\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429880 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=429880\">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=kx%5E2%2Bkx%2B5=0+ ALIGN=MIDDLE  ALT=\"kx%5E2%2Bkx%2B5=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4ac+=+0 ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the solution will have equal roots or only one solution\r<BR>\n" );
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document.write( "here <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+k ALIGN=MIDDLE  ALT=\"b+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+k ALIGN=MIDDLE  ALT=\"a+=+k\"   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;\" >\r<BR>\n" );
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document.write( "so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2+-+4%2Ak%2A5+=+0 ALIGN=MIDDLE  ALT=\"k%5E2+-+4%2Ak%2A5+=+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%5E2+-+20k+=+0 ALIGN=MIDDLE  ALT=\"k%5E2+-+20k+=+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%28k+-+20%29+=+0 ALIGN=MIDDLE  ALT=\"k%28k+-+20%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C%3E0 ALIGN=MIDDLE  ALT=\"k%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > product will be equal to zero if \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+-+20=0 ALIGN=MIDDLE  ALT=\"k+-+20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=20 ALIGN=MIDDLE  ALT=\"k+=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then you have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%5E2%2B20x%2B5=0+ ALIGN=MIDDLE  ALT=\"20x%5E2%2B20x%2B5=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check if the roots are equal:\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-20+%2B-+sqrt%2820%5E2-4%2A20%2A5+%29%29%2F%282%2A20%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+sqrt%2820%5E2-4%2A20%2A5+%29%29%2F%282%2A20%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=x+=+%28-20+%2B-+sqrt%28400-400+%29%29%2F40+ ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+sqrt%28400-400+%29%29%2F40+\"   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+=+%28-20+%2B-+sqrt%280%29%29%2F40+ ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+sqrt%280%29%29%2F40+\"   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+=+%28-20+%2B-+0%29%2F40+ ALIGN=MIDDLE  ALT=\"x+=+%28-20+%2B-+0%29%2F40+\"   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+=+-20%2F40+ ALIGN=MIDDLE  ALT=\"x+=+-20%2F40+\"   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+=+-1%2F2+ ALIGN=MIDDLE  ALT=\"x+=+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......so, we have only one root\r<BR>\n" );
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document.write( "see it on a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+20x%5E2%2B20x%2B5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+20x%5E2%2B20x%2B5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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