document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6287>Question 6287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the value of k for which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5xy%2B3y%5E2%2B3x%2B4y%2Bk=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5xy%2B3y%5E2%2B3x%2B4y%2Bk=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >represent a pair of straight lines </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3364 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=3364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  2x^2+5xy-3y^2+3x+4y+k =0,<BR>\n" );
document.write( " Factoring the first three terms, we have<BR>\n" );
document.write( " (2x + 3y)(x + y) + 3x + 4y + k = 0<BR>\n" );
document.write( " Assume the left polynomial can be factored into <BR>\n" );
document.write( "  (2x + y+ a)(x + 3y+b) =  (2x + 3y)(x + y) + (a+2b)x + (3a+b)y + k<BR>\n" );
document.write( " Comparing the coefficients,we have<BR>\n" );
document.write( " k = ab and<BR>\n" );
document.write( " a+2b = 3 , 3a+b = 4 <BR>\n" );
document.write( " Solve the system for a,b: we have a = 1 and b = 1<BR>\n" );
document.write( " Hence, k = ab = 1 \r<BR>\n" );
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document.write( " Plz check the answer by yourself.\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );