document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767460>Question 767460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Sir/Madam,<BR>\n" );
document.write( "Good day!  Kindly help me with this problem, I sent almost the same problem but committed an error of tying the wrong value.  Here it goes...<BR>\n" );
document.write( "Find the value of k so that the equation 3x^2-4kx+k =0 will have real roots. Thank you very much for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467630 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=467630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:<BR>\n" );
document.write( "Find the value of k so that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-4kx%2Bk+=0 ALIGN=MIDDLE  ALT=\"3x%5E2-4kx%2Bk+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have real roots<BR>\n" );
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document.write( "A:<BR>\n" );
document.write( "The quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > have real roots if the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > is greater than or equal to zero.<BR>\n" );
document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-4kx%2Bk+=0 ALIGN=MIDDLE  ALT=\"3x%5E2-4kx%2Bk+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a = 3, b = -4k and c = k.<BR>\n" );
document.write( "The discriminant is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4k%29%5E2+-+4%283%29%28k%29 ALIGN=MIDDLE  ALT=\"%28-4k%29%5E2+-+4%283%29%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16k%5E2+-+12k ALIGN=MIDDLE  ALT=\"16k%5E2+-+12k\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16k%5E2+-+12k ALIGN=MIDDLE  ALT=\"16k%5E2+-+12k\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8805; 0<BR>\n" );
document.write( "4k(4k - 3) &#8805; 0<BR>\n" );
document.write( "Using sign test<BR>\n" );
document.write( "k &#8804; 0  OR k &#8805; 3/4<BR>\n" );
document.write( "In interval notation: (-&#8734;, 0] &#8746; [ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &#8734;) </SPAN>\n" );
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