document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150727>Question 1150727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the equation 3bx^2 + 6bx = ax + 2a has two solutions for x and that the sum and the product of these solutions are equal, then b/a = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772141 by </B><A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><B>amarjeeth123(570)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><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=772141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are given that the equation 3bx^2 + 6bx = ax + 2a has two solutions for x and<BR>\n" );
document.write( "the sum and the product of the roots are equal.<BR>\n" );
document.write( "The given equation can be rewritten as 3bx^2+(6b-a)x+(-2a)=0<BR>\n" );
document.write( "The sum of the roots=(a-6b)/3b<BR>\n" );
document.write( "Product of the roots=(-2a)/3b<BR>\n" );
document.write( "Since both of them are equal we get,a-6b=-2a<BR>\n" );
document.write( "3a-6b=0<BR>\n" );
document.write( "3a=6b<BR>\n" );
document.write( "a=2b<BR>\n" );
document.write( "b/a=1/2.<BR>\n" );
document.write( "Verification:<BR>\n" );
document.write( "Put b=1 and a=2<BR>\n" );
document.write( "The equation becomes 3x^2+6x=2x+4<BR>\n" );
document.write( "3x^2+4x-4=0<BR>\n" );
document.write( "Sum of the roots=-4/3<BR>\n" );
document.write( "Product of the roots=-4/3<BR>\n" );
document.write( "Hence the solution is correct.<BR>\n" );
document.write( "b/a=1/2. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );