document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197405>Question 1197405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I know if the quadratic equation has two real solutions, a double root, or no real solution, without solving the equation in a discriminant way? here are some examples \r<BR>\n" );
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document.write( "2a2+3a+1=0<BR>\n" );
document.write( "2)2a(a  -  3)  -  3=3<BR>\n" );
document.write( "3a2  -  2a(a  -  2)2  -  4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830658 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Why without discriminant?\r<BR>\n" );
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document.write( "Could you factorize your equations?\r<BR>\n" );
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document.write( "Your last equation is not quadratic.<BR>\n" );
document.write( "3a^2-2a(a-2)^2-4=0\r<BR>\n" );
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document.write( "3a^2-2a(a^2-4a+4)-4=0\r<BR>\n" );
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document.write( "3a^2-2a^3+8a^2-8a-4=0\r<BR>\n" );
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document.write( "-2a^3+11a^2-8a-4=0\r<BR>\n" );
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document.write( "3a^3-11a^2+8a+4=0 </SPAN>\n" );
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