document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825876>Question 825876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what values of k does 2x^2 - 5x - k = 0  have no real roots?<BR>\n" );
document.write( "Can you please help me out? Thanks so much in advance:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497661 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E2+-+5x+-+k+=+0+ ALIGN=MIDDLE  ALT=\"+2x%5E2+-+5x+-+k+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the 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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2+ ALIGN=MIDDLE  ALT=\"+a+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-5+ ALIGN=MIDDLE  ALT=\"+b+=+-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-k+ ALIGN=MIDDLE  ALT=\"+c+=+-k+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the roots are imaginary when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is negative. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+ ALIGN=MIDDLE  ALT=\"+b%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is always positive.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2Aa%2Ac+%3E+b%5E2+ ALIGN=MIDDLE  ALT=\"+4%2Aa%2Ac+%3E+b%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2A2%2A%28-k%29+%3E+%28-5%29%5E2+ ALIGN=MIDDLE  ALT=\"+4%2A2%2A%28-k%29+%3E+%28-5%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8%2Ak+%3E+25+ ALIGN=MIDDLE  ALT=\"+-8%2Ak+%3E+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+%3C+-25%2F8+ ALIGN=MIDDLE  ALT=\"+k+%3C+-25%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "( note that I had to reverse the inequality sign<BR>\n" );
document.write( "when I divided by a negative number )<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+-25%2F8+ ALIGN=MIDDLE  ALT=\"+k+=+-25%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+%28-5%29%5E2+-+4%2A2%2A%28-k%29+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+%28-5%29%5E2+-+4%2A2%2A%28-k%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+25+-+4%2A2%2A%28-%28-25%2F8%29%29+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+25+-+4%2A2%2A%28-%28-25%2F8%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+25+-+25+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+25+-+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+0+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That means there is 1 real root<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+-26%2F8+ ALIGN=MIDDLE  ALT=\"+k+=+-26%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+-13%2F4+ ALIGN=MIDDLE  ALT=\"+k+=+-13%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+%28-5%29%5E2+-+4%2A2%2A%28-k%29+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+%28-5%29%5E2+-+4%2A2%2A%28-k%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+25+-+4%2A2%2A%28-%28-13%2F4%29%29+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+25+-+4%2A2%2A%28-%28-13%2F4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+25+-+26+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+25+-+26+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+-1+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That means there are 2 imaginary roots\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );