document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030084>Question 1030084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For how many integers b does the inequality z^2 + bz + 15 < 0 have no real solutions z? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644983 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644983\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You want the discriminant to be negative or zero so that the graph of z^2 + bz + 15 lies completely above the z-axis (i.e. is always non-negative).\r<BR>\n" );
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document.write( "Therefore we want <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large b^2 - 4 \cdot 1 \cdot 15 \le 0\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large b^2 \le 60\">. This works for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large b = \pm 0, \pm 1, \ldots, \pm 7\"> or 15 integers. </SPAN>\n" );
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