document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28934>Question 28934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "I'm currently studying solving quadratic inequalities, and I'm having a bit of trouble.\r<BR>\n" );
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document.write( "I'm trying to solve 1/2x^2 + 3x (less than or equal to) -6. Since I couldn't factor the equation, I tried using the quadratic formula, however I got a complex number. I'm not exactly sure how to test the complex numbers, so I'm a bit lost on how to solving this.\r<BR>\n" );
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document.write( "Thanks for any help you can provide! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18106 by </B><A HREF=/tutors/aboutme.mpl?userid=Fermat><B>Fermat(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fermat><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=Fermat><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18106\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There's a mistake in this question.<BR>\n" );
document.write( "As you found out, you will end up with complex roots.<BR>\n" );
document.write( "That's the problem!<BR>\n" );
document.write( "You can't compare complex numbers. Unless they are both totally real or totally imaginary.<BR>\n" );
document.write( "You can't have an inequality such as 3 < 2i, or even 2 + 5i > 1 - 3i.<BR>\n" );
document.write( "You can test this out by graphing the curve of (1/2)x² + 3x and see where its lowest point is wrt the line y = -6.<BR>\n" );
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document.write( "As you can see, the line y = -6 is less than the curve (1/2)x² + 3x at all times, so that inequality never holds. </SPAN>\n" );
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