document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27170>Question 27170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was givin the following question.\r<BR>\n" );
document.write( "\n" );
document.write( "The quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2Bkx%2Bk=0+ ALIGN=MIDDLE  ALT=\"+x%5E2%2Bkx%2Bk=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > has no real roots for x.\r<BR>\n" );
document.write( "\n" );
document.write( "1) Write down the discriminant of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2Bkx%2Bk+ ALIGN=MIDDLE  ALT=\"+x%5E2%2Bkx%2Bk+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms of k.\r<BR>\n" );
document.write( "\n" );
document.write( "2) Hence find the set of values that k can take.\r<BR>\n" );
document.write( "\n" );
document.write( "If somebody could help me. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14778 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=14778\">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=x%5E2+%2B+kx+%2B+k+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+kx+%2B+k+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > has no real roots<BR>\n" );
document.write( "that means the roots are imaginary- they involve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is i.<BR>\n" );
document.write( "The quadratic formula is:<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( "where the equation is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5E2+%2Bb%2Ax+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"a%2Ax%5E2+%2Bb%2Ax+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+k%2Ax+%2B+k+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+k%2Ax+%2B+k+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so,<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = k<BR>\n" );
document.write( "c = k<BR>\n" );
document.write( "substitute these in the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-k+%2B-+sqrt%28+k%5E2-4%2A1%2Ak+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-k+%2B-+sqrt%28+k%5E2-4%2A1%2Ak+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-k+%2B-+sqrt%28+k%5E2-4%2Ak+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-k+%2B-+sqrt%28+k%5E2-4%2Ak+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The discriminant, which is everything under the square root sign,<BR>\n" );
document.write( "needs to be negative if the roots are imaginary<BR>\n" );
document.write( "that means <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%5E2+-+4%2Ak++%3C+0 ALIGN=MIDDLE  ALT=\"+k%5E2+-+4%2Ak++%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factoring<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%28k+-+4%29+%3C+0 ALIGN=MIDDLE  ALT=\"+k%28k+-+4%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k can't be greater than 4 or equal to 4.<BR>\n" );
document.write( "that would make the inequality false<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%284+-+4%29+%3C+0 ALIGN=MIDDLE  ALT=\"+4%284+-+4%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2A+0+%3C+0 ALIGN=MIDDLE  ALT=\"4+%2A+0+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "not true<BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%285+-+4%29+%3C+0 ALIGN=MIDDLE  ALT=\"+5%285+-+4%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2A+1+%3C+0 ALIGN=MIDDLE  ALT=\"5+%2A+1+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "not true either<BR>\n" );
document.write( "k can't be zero or less than zero either<BR>\n" );
document.write( "I would get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0%280+-+4%29+%3C+0 ALIGN=MIDDLE  ALT=\"+0%280+-+4%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "not true<BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%28-1+-+4%29+%3C+0 ALIGN=MIDDLE  ALT=\"+-1%28-1+-+4%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%2A+-5+%3C+0 ALIGN=MIDDLE  ALT=\"-1+%2A+-5+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "not true either<BR>\n" );
document.write( "so, that means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%3E+k+%3E+0 ALIGN=MIDDLE  ALT=\"4+%3E+k+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "meaning k is between 0 and 4 but doesn't include 0 or 4. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );