document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32757>Question 32757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dealing with contradictions:  If a, b, and c are nonzero real numbers such that a>0 and the equation ax^2+bx+c has no real solutions, then show that ax^2+bx+c<0 cannot be true for all values of x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19261 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=19261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> AX^2+BX+C=0...HAS NO REAL SOLUTION...SO DISCRIMINANT = B^2-4AC ..IS<BR>\n" );
document.write( "NEGATIVE....OR....4AC-B^2 IS POSITIVE<BR>\n" );
document.write( "LET F(X)=AX^2+BX+C=A{X^2+BX/A+C/A}=A[{X^2+2(X)(B/2A)+(B/2A)^2}-(B/2A)^2+(C/A)]<BR>\n" );
document.write( "=A[{X+(B/A)}^2}+{(C/A)-B^2/4A^2}]=A[{X+(B/A)}^2+{(4AC-B^2)/4A^2}]<BR>\n" );
document.write( "SO F(x)=A..SINCE {X+(B/A)}^2 IS<BR>\n" );
document.write( "ALWAYS POSITIVE BEING A PERFECT SQUAREAND {(4AC-B^2)} IS POSITIVE AS<BR>\n" );
document.write( "SHOWN ABOVE AND 4A^2 IS ALSO POSITIVE BEING A PERFECT SQUARE...<BR>\n" );
document.write( "HENCE F(X) IS ONLY DEPENDENT ON SIGN OF A...<BR>\n" );
document.write( "F(X) IS POSITIVE IF A IS POSITIVE ..AND<BR>\n" );
document.write( "F(X) IS NEGATIVE IF A IS NEGATIVE..<BR>\n" );
document.write( "SO IF WE ARE GIVEN THAT A >0..OR POSITIVE THEN<BR>\n" );
document.write( "F(X)=AX^2 + BX + C CAN NOT BE NEGATIVE </SPAN>\n" );
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