document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=678341>Question 678341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of b so that the equation will have exactly one rational solution.  \r<BR>\n" );
document.write( "\n" );
document.write( "12p^2+bp+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 #421310 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=421310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the value of b so that the equation will have exactly one rational solution.  \r<BR>\n" );
document.write( "\n" );
document.write( "12p^2+bp+3=0<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "2nd order equations ALWAYS have 2 solutions.<BR>\n" );
document.write( "Sometimes it's the same solution, multiplicity 2, but there are 2 solutions.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "To have the same solution twice, the discriminant = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4ac+=+0 ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4%2A12%2A3+=+0 ALIGN=MIDDLE  ALT=\"b%5E2+-+4%2A12%2A3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+144 ALIGN=MIDDLE  ALT=\"b%5E2+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = -12<BR>\n" );
document.write( "b = +12<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );