document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767720>Question 767720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> DEar  Sir/Madam,<BR>\n" );
document.write( "Please help me in solving this problem, I am not much familiar with finding the range of values of k.  The problem is:  Find the range of values of k so that the equation x^2+2kx+3/4 - k will not intersect the y-axis?  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 #467792 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=467792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "There are no real number values of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE k\"> such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)\ =\ x^2\ +\ 2kx\ +\ \frac{3}{4}\ -\ k\">.  For any quadratic function of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE ax^2\ +\ bx\ +\ c\">, the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-intercept is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (0,\,c)\">\r<BR>\n" );
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document.write( "Since the real values of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-coordinates of points on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-axis are in the range <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,\,\infty\right)\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \forall\ k\ \in\ \mathbb{R},\ \left(\frac{3}{4}\ -\ k\right)\ \in\ \left(-\infty,\,\infty\right)\">, there is no possible value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE k\"> such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{3}{4}\ -\ k\right)\"> does not map to some available <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">.\r<BR>\n" );
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document.write( "By the way, be careful with your terminology.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2\ +\ 2kx\ +\ \frac{3}{4}\ -\ k\"> is NOT an equation.  Equations have equals signs in them; hence the name.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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