document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154861>Question 154861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me:\r<BR>\n" );
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document.write( "1. How many solutions exist for a quadratic equation?  How do we detemine whether the solutions are real or complex?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114025 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=114025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How many solutions exist for a quadratic equation?  <BR>\n" );
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document.write( "The number of roots of a polynomial equation is equal to the degree of the polynomial (the exponent of the leading term). <BR>\n" );
document.write( "Quadratic equations are of degree 2, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "They have two (2) roots.<BR>\n" );
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document.write( "How do we detemine whether the solutions are real or complex? <BR>\n" );
document.write( "Use the discriminant.<BR>\n" );
document.write( "For the general quadratic equation, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the discriminant is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=b%5E2-4ac ALIGN=MIDDLE  ALT=\"D=b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%3E0 ALIGN=MIDDLE  ALT=\"D%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then you have two distinct real roots.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-7x%2B10=%28x-2%29%28x-5%29 ALIGN=MIDDLE  ALT=\"x%5E2-7x%2B10=%28x-2%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=49-4%2810%29=9 ALIGN=MIDDLE  ALT=\"D=49-4%2810%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2 real roots, x=2,5 .<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=0 ALIGN=MIDDLE  ALT=\"D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you have a double root, one real root occurring twice <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1=%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=4-4%281%29=0 ALIGN=MIDDLE  ALT=\"D=4-4%281%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2 real roots, x=1,1.<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%3C0 ALIGN=MIDDLE  ALT=\"D%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you have two complex roots, that are complex conjugates.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B1=%28x%2Bi%29%28x-i%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B1=%28x%2Bi%29%28x-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=0-4%281%29=-4 ALIGN=MIDDLE  ALT=\"D=0-4%281%29=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2 complex roots, x=i,-i.<BR>\n" );
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