document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767452>Question 767452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Sir/Madam,<BR>\n" );
document.write( "Good day! Kindly help me on this problem:<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 #467627 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=467627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the value of k so that the equation 3x^2-4kx+k = 0 will have real roots.<BR>\n" );
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document.write( "Equation will have 2 equal real roots when the discriminant=0<BR>\n" );
document.write( "a=3, b=-4k, c=k<BR>\n" );
document.write( "discriminant=b^2-4*a*c=(-4k)^2-4*3*k=16k^2-12k=0<BR>\n" );
document.write( "k(16k-12)=0<BR>\n" );
document.write( "k=0 (reject)<BR>\n" );
document.write( "k=12/16=3/4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "solve for x with k=3/4<BR>\n" );
document.write( "3x^2-4kx+k=3x^2-3x+3/4=0<BR>\n" );
document.write( "12x^2-12x+3=0<BR>\n" );
document.write( "solve for x by quadratic formula:<BR>\n" );
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;\" ><BR>\n" );
document.write( "a=12, b=-12, c=3<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "x=0.5 (multiplicity 2)<BR>\n" );
document.write( " </SPAN>\n" );
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