document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=679859>Question 679859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for each equation, determine what type of number the solutions are and how many solutions exists.\r<BR>\n" );
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document.write( "x^2+10x+11=0 \r<BR>\n" );
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document.write( "i've tried to do it with the quadratic equation but im not sure if i have to use the quadratic equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #422082 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=422082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For what they are asking, you just need the part of the<BR>\n" );
document.write( "quadratic formula called the \" discriminant \". It is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is inside a square root sign.<BR>\n" );
document.write( "The rules are:<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+0+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 1 real solution<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+%3C+0+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 2 imaginary solutions<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+%3E+0+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+%3E+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 2 real solutions<BR>\n" );
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document.write( "That's all you need for this problem.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B10x+%2B11=0+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B10x+%2B11=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+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+10+ ALIGN=MIDDLE  ALT=\"+b+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+11+ ALIGN=MIDDLE  ALT=\"+c+=+11+\"   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+-+4%2Aa%2Ac+=+10%5E2+-+4%2A1%2A11+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+10%5E2+-+4%2A1%2A11+\"   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+-+4%2Aa%2Ac+=+100+-+44+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+100+-+44+\"   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+-+4%2Aa%2Ac+=+56+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+56+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is greater than zero, so there are 2 real solutions<BR>\n" );
document.write( "Here's a plot of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-16%2C+10%2C+x%5E2+%2B+10x+%2B+11+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-16%2C+10%2C+x%5E2+%2B+10x+%2B+11+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "You can see that the solutions are (2) real negative numbers<BR>\n" );
document.write( "You can get the fact they are negative from the rest of the quadratic formula:<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( "  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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