document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=536504>Question 536504</A>: <I><SPAN STYLE=\"word-break: break-all;\">             One of the roots of the quadratic equation ax2+bx+c=0 is twice the other.Show that 2b2=9ac<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352624 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=352624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r and 2r be the roots. By Vieta's formulas, the sum of the roots is -b/a and the product of the roots is c/a. We have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3r = -\frac{b}{a}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2r^2 = \frac{c}{a}\">\r<BR>\n" );
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document.write( "Squaring the first equation,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 9r^2 = \frac{b^2}{a^2} \Rightarrow 2r^2 = \frac{2b^2}{9a^2}\">\r<BR>\n" );
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document.write( "This is equal to c/a so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2b^2}{9a^2} = \frac{c}{a}\"> This can be simplified and rearranged to obtain 2b^2 = 9ac. </SPAN>\n" );
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