document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=427879>Question 427879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What happens when the quadratic equation is no solution? For example,<BR>\n" );
document.write( "x2+6x+10=0<BR>\n" );
document.write( "A=1 B=6 C=10<BR>\n" );
document.write( "D= b2-4ac<BR>\n" );
document.write( "D=62-4(10)=-4<BR>\n" );
document.write( "-4<0 no real solutions\r<BR>\n" );
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document.write( "What now? <BR>\n" );
document.write( "Thank you :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297503 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=297503\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Solving by the Quadratic Formula\r<BR>\n" );
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document.write( "Since this formula is somewhat long and complicated, it is best to evaluate it in two smaller pieces by first evaluating the thing inside the radical,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and then put the result into the formula \r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "The quantity<BR>\n" );
document.write( "b^2-4ac\r<BR>\n" );
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document.write( "even has a name. <BR>\n" );
document.write( "It is called the discriminant. And there is another advantage to computing it first. Since it is what is in the radical, it can't be negative if there are going to be solutions to the equation, because you can't take a square root of a negative number, (unless you use the imaginary numbers, and we're not yet ready for them here) so if the discriminant comes out negative, then you don't have to do any more work, and all you have to do is write \"no solution\" on your paper and you are done. Sometimes you can determine this quite quickly by estimating, particularly if a and c are very large and b is small. \r<BR>\n" );
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document.write( "Example <BR>\n" );
document.write( "Problem: Solve the equation. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2+-2x%2B27=0 ALIGN=MIDDLE  ALT=\"6x%5E2+-2x%2B27=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solution: \r<BR>\n" );
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document.write( "here we have no solution because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is very small in comparison to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=27 ALIGN=MIDDLE  ALT=\"c=27\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so you don't <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=even ALIGN=MIDDLE  ALT=\"even\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+have ALIGN=MIDDLE  ALT=\"+have\"   DISABLED_style= \"max-width:90%; height:auto;\" > to compute the discriminant to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=see+ ALIGN=MIDDLE  ALT=\"see+\"   DISABLED_style= \"max-width:90%; height:auto;\" >that it is going to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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