document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071181>Question 1071181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the discriminant. how many real solutions does the equation have? -4x^2-4=8x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686103 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=686103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Discriminant?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2-4=8x ALIGN=MIDDLE  ALT=\"-4x%5E2-4=8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2-8x-4=0 ALIGN=MIDDLE  ALT=\"-4x%5E2-8x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now discriminant?  But here, not really needed because you know that quadratic expression is factorable.    ONE REAL SOLUTION.  Why?  You know the quadratic there is a perfect square.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x%2B1%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--<BR>\n" );
document.write( "Discriminant here is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2-4%2A1%2A1=4-4=highlight%280%29 ALIGN=MIDDLE  ALT=\"2%5E2-4%2A1%2A1=4-4=highlight%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That is what you get when the quadratic expression is a perfect square trinomial. </SPAN>\n" );
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