document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80076>Question 80076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What values of b in the following equations will give one or more real number solutions?\r<BR>\n" );
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document.write( "a). 3x^2+bx-3=0<BR>\n" );
document.write( "b). 5x^2+bx+1=0<BR>\n" );
document.write( "c). -3x^2+bx-3=0\r<BR>\n" );
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document.write( "what is a rule for judging if an equation has solutions by looking at it in standard form?\r<BR>\n" );
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document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57435 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=57435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What values of b in the following equations will give one or more real number solutions?<BR>\n" );
document.write( "Look at b^2-4ac for each equation: <BR>\n" );
document.write( "a). 3x^2+bx-3=0<BR>\n" );
document.write( "b^2-4ac<BR>\n" );
document.write( "=b^2-4*3*-3<BR>\n" );
document.write( "=b^2+36<BR>\n" );
document.write( "This expression will be non-negative for all values of \"b\".<BR>\n" );
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document.write( "b). 5x^2+bx+1=0<BR>\n" );
document.write( "b^2-4ac<BR>\n" );
document.write( "=b^2-4*5*1<BR>\n" );
document.write( "=b^2-20<BR>\n" );
document.write( "This expression will be non-negative for all b>=2sqrt5 or less than -2sqrt5<BR>\n" );
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document.write( "c). -3x^2+bx-3=0 <BR>\n" );
document.write( "b^2-4ac<BR>\n" );
document.write( "=b^2-4*-3*-3<BR>\n" );
document.write( "=b^2-36<BR>\n" );
document.write( "This expression be non-negative for all b >=6 or <= than -6<BR>\n" );
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document.write( "what is a rule for judging if an equation has solutions by looking at it in standard form?<BR>\n" );
document.write( "b^2>=4ac<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
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