document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=569254>Question 569254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you know if a quadratic equation will have one, two, or no sloution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367330 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=367330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> All quadratics will have two (complex) solutions. However, to determine if they're real or if there are duplicate roots, you'll have to take the discriminant, defined as delta = b^2 - 4ac.\r<BR>\n" );
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document.write( "Recall the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\"> \r<BR>\n" );
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document.write( "If b^2 - 4ac > 0, then the square root will be defined and you will have two real solutions.\r<BR>\n" );
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document.write( "If b^2 - 4ac = 0, then the square root will be equal to 0, and you'll have a duplicate root (-b/2a).\r<BR>\n" );
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document.write( "If b^2 - 4ac < 0, then the square root will be a complex number and you'll have two complex solutions (by complex, I mean Im(x) is not equal to 0). </SPAN>\n" );
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