document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102279>Question 102279</A>: <I><SPAN STYLE=\"word-break: break-all;\"> decide all values of b in the following equations that will<BR>\n" );
document.write( "give one or more real number solutions.<BR>\n" );
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 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74328 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=74328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> decide all values of b in the following equations that will<BR>\n" );
document.write( "give one or more real number solutions.<BR>\n" );
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<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Each of these is a quadratic equation.<BR>\n" );
document.write( "To have Real Number solutions the discriminant must be > or = to zero.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "a) a=3,b=b,c=-3<BR>\n" );
document.write( "b^2-4ac>=0<BR>\n" );
document.write( "b^2-4*3*-3>=0<BR>\n" );
document.write( "b^2+36 >=0<BR>\n" );
document.write( "b^2 >= -36<BR>\n" );
document.write( "But b^2 is always >= -36 so b may have any Real Number value.<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Follow the same procedure on questions b) and c).<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );