document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=16705>Question 16705</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all values for k such that the equation 3x squared - 2x + k = 0  has imaginary roots </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8209 by </B><A HREF=/tutors/aboutme.mpl?userid=xcentaur><B>xcentaur(357)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=xcentaur><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=8209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x^2 - 2x + k = 0\r<BR>\n" );
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document.write( "For imaginary roots, discriminant(D) must be less than zero.\r<BR>\n" );
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document.write( "D=b^2-4ac is the discriminant.\r<BR>\n" );
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document.write( "D= (-2)^2 -4(3)(k)<BR>\n" );
document.write( " = 4 - 12k<BR>\n" );
document.write( "This must be less than zero.\r<BR>\n" );
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document.write( "Therefore, 4 - 12k < 0<BR>\n" );
document.write( "4<12k<BR>\n" );
document.write( "1<3k<BR>\n" );
document.write( "1/3<k\r<BR>\n" );
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document.write( "Hence for all values of k which are less than 1/3,the roots will be imaginary.\r<BR>\n" );
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document.write( "<P>For k=1/3,roots will be real and equal. All values of k greater than 1/3 will result in real distinct roots.\r<BR>\n" );
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document.write( "<P>Hope this helps,<BR>\n" );
document.write( "Prabhat </SPAN>\n" );
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