document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=457996>Question 457996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation 2(x^2+12)+kx=0<BR>\n" );
document.write( "where k <0 has roots a and b where a-b=4.Find the value of k </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #314143 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><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=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=314143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x^2 + kx + 24 = 0\r<BR>\n" );
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document.write( "Two roots a and b where a - b = 4 so a must be the larger.\r<BR>\n" );
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document.write( "We know that<BR>\n" );
document.write( "a = (-k + sqrt(k^2 - 192))/4<BR>\n" );
document.write( "b = (-k - sqrt(k^2 - 192))/4\r<BR>\n" );
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document.write( "Therefore a - b = 2 (sqrt(k^2 - 192))/4 = 4<BR>\n" );
document.write( "sqrt(k^2 - 192) = 8<BR>\n" );
document.write( "k^2 - 192 = 64<BR>\n" );
document.write( "k^2 = 192 + 64<BR>\n" );
document.write( "k^2 = 256<BR>\n" );
document.write( "k = -16 (k<0 so cannot be 16)\r<BR>\n" );
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document.write( "Check<BR>\n" );
document.write( "2x^2 - 16x + 24 = 0<BR>\n" );
document.write( "x^2 - 8x + 12 = 0<BR>\n" );
document.write( "(x - 6)(x - 2) = 0<BR>\n" );
document.write( "a = 6; b = 2<BR>\n" );
document.write( "a - b = 4<BR>\n" );
document.write( " </SPAN>\n" );
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