document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172073>Question 172073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how and when would you use the \"discriminant\"? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127114 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127114\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The discriminant is the part of the quadratic formula that is under the radical sign.\r<BR>\n" );
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document.write( "Quadratic formula:  <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;\" > \r<BR>\n" );
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document.write( "So the discriminant is:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA+=+b%5E2-4ac ALIGN=MIDDLE  ALT=\"DELTA+=+b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the discriminant to determine the character of the roots of a quadratic equation.\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA=0 ALIGN=MIDDLE  ALT=\"DELTA=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > there is one real number root with a multiplicity of 2.\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA%3E0 ALIGN=MIDDLE  ALT=\"DELTA%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > there are two real number roots.\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA%3C0 ALIGN=MIDDLE  ALT=\"DELTA%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > there is a conjugate pair of complex roots of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B-bi ALIGN=MIDDLE  ALT=\"a%2B-bi\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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