document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180170>Question 1180170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what values of k will the graph of y = 9x^2+3kx+k have no x-intercepts? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809778 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809778\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "When the discriminant b^2-4ac is negative.<br><BR>\n" );
document.write( "a=9<BR>\n" );
document.write( "b=3k<BR>\n" );
document.write( "c=k<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%283k%29%5E2-4%289%29%28k%29=9k%5E2-36k ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283k%29%5E2-4%289%29%28k%29=9k%5E2-36k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9k%5E2-36k%3C0 ALIGN=MIDDLE  ALT=\"9k%5E2-36k%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2-4k%3C0 ALIGN=MIDDLE  ALT=\"k%5E2-4k%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%28k-4%29%3C0 ALIGN=MIDDLE  ALT=\"k%28k-4%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The graph of k(k-4) is a parabola that opens upward, with zeros at k=0 and k=4.  So the value of the expression is negative only between 0 and 4.<br><BR>\n" );
document.write( "ANSWER: 0 < k < 4<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );