document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120096>Question 120096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! May I have some help with this equation?\r<BR>\n" );
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document.write( "Find all values of k that ensure that the given equation has exactly one solution.\r<BR>\n" );
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document.write( "8x2 + kx + 7 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88023 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=88023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a case where you use the quadratic equation and make<BR>\n" );
document.write( "sure that the discriminant, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4ac ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > is zero<BR>\n" );
document.write( "That guarantees that there is only one solution.<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 equation is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x2+%2B+kx+%2B+7+=+0 ALIGN=MIDDLE  ALT=\"8x2+%2B+kx+%2B+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+8 ALIGN=MIDDLE  ALT=\"a+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+k ALIGN=MIDDLE  ALT=\"b+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+7 ALIGN=MIDDLE  ALT=\"c+=+7\"   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+-+4ac+=+0 ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac+=+0\"   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+-+4%2A8%2A7+=+0 ALIGN=MIDDLE  ALT=\"k%5E2+-+4%2A8%2A7+=+0\"   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+-+224+=+0 ALIGN=MIDDLE  ALT=\"k%5E2+-+224+=+0\"   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+=+224 ALIGN=MIDDLE  ALT=\"k%5E2+=+224\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+sqrt%28224%29 ALIGN=MIDDLE  ALT=\"k+=+sqrt%28224%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+sqrt%2814%2A16%29 ALIGN=MIDDLE  ALT=\"k+=+sqrt%2814%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%2B4%2Asqrt%2814%29 ALIGN=MIDDLE  ALT=\"k+=+%2B4%2Asqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-4%2Asqrt%2814%29 ALIGN=MIDDLE  ALT=\"k+=+-4%2Asqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer </SPAN>\n" );
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