document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997637>Question 997637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B8x%2Bk=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B8x%2Bk=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , for what values of k will the equation have a repeated root, 2 real roots, and 3 values of k that will give the equation rational roots. I understand what it means to have those types of roots, I just don't understand how you would get to those specific answers. Like, I know how to find and imaginary root for this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%5B-infinite%3Ck%3Cless+than+0%5D+ ALIGN=MIDDLE  ALT=\"+%5B-infinite%3Ck%3Cless+than+0%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > . Would that be right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615642 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The discriminant of your equation is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2-4%2A4%2Ak ALIGN=MIDDLE  ALT=\"8%5E2-4%2A4%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Simplified, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64-16k ALIGN=MIDDLE  ALT=\"64-16k\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set discriminant to 0 to find what k gives two repeated roots.  Solve for k.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set discriminant to be greater than 0 to find what k gives two unique roots.  Solve for k.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--<BR>\n" );
document.write( "This, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%5B-infinite%3Ck%3Cless+than+0%5D+ ALIGN=MIDDLE  ALT=\"+%5B-infinite%3Ck%3Cless+than+0%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , did not render because  bunch of notation wrong......<BR>\n" );
document.write( "In pure text, it must read  -infinity lessThan k lessThan 0,... unfortunately this will fail if done on this site page in the proper pure text symbolism, but the proper symbolism WILL render:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity%3Ck%3C0 ALIGN=MIDDLE  ALT=\"-infinity%3Ck%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "To see that, click the View Source or Show Source link. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );