document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=766331>Question 766331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^2+4x+c=0 <BR>\n" );
document.write( "what value of c does the equation have one real root and what range of value does it have two roots, fo what range of values does the equation have two complex.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466850 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=466850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general solution, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4%2B-sqrt%284%2A4-4%2A1%2Ac%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-4%2B-sqrt%284%2A4-4%2A1%2Ac%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "contains an expression, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2-4c ALIGN=MIDDLE  ALT=\"4%5E2-4c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That is the DISCRIMINANT.  It is written in the square root function.  \r<BR>\n" );
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document.write( "Discriminant = 0, then equation has one real root.<BR>\n" );
document.write( "Discriminant greater than zero, then equation has two real roots.<BR>\n" );
document.write( "Discriminant less than zero, then the equation has two complex roots with imaginaries.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2B-sqrt%284-c%29 ALIGN=MIDDLE  ALT=\"x=-2%2B-sqrt%284-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  when simplified.\r<BR>\n" );
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document.write( "c=4 makes x be exactly one solution because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284-4%29=0 ALIGN=MIDDLE  ALT=\"sqrt%284-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "c<4 makes x be either of two real solutions because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284-c%29 ALIGN=MIDDLE  ALT=\"sqrt%284-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will itself be a real value.<BR>\n" );
document.write( "c>4 makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284-c%29 ALIGN=MIDDLE  ALT=\"sqrt%284-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > be imaginary, and there be two complex roots solutions for x with imaginary components. </SPAN>\n" );
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