document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=481782>Question 481782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi i need some help. here is the qns\r<BR>\n" );
document.write( "\n" );
document.write( "Find the values of k for which the quadratic equation 9x^2-kx+(k-7)=0 has<BR>\n" );
document.write( "(i) one positive and one negative root<BR>\n" );
document.write( "(ii) one root twice the value of the other </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329867 by </B><A HREF=/tutors/aboutme.mpl?userid=mathstutor494><B>mathstutor494(120)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathstutor494><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=mathstutor494><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=329867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9x^2-kx+(k-7)=0\r<BR>\n" );
document.write( "\n" );
document.write( "1. Condition for a quadratic equation ax^2+bx+c=0 to have one positive and one negative root is that discriminant b^2-4ac > 0\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting values of a, b & c from the problem, we get<BR>\n" );
document.write( "(-k)^2 - 4*9*(k-7)>0<BR>\n" );
document.write( "k^2- 36k + 252 >0\r<BR>\n" );
document.write( "\n" );
document.write( "Solving above quadratic equation results in k= 42, -6<BR>\n" );
document.write( "Hence k=42\r<BR>\n" );
document.write( "\n" );
document.write( "2. Sum of the roots S = x1+x2 = -b/a and product of roots P=x1*x2=c/a\r<BR>\n" );
document.write( "\n" );
document.write( "Here x1 = x and x2 = 2x\r<BR>\n" );
document.write( "\n" );
document.write( "So S = x+2x = -(-k)/9 and P = x*2x = (k-7)/9\r<BR>\n" );
document.write( "\n" );
document.write( "Accordingly S= 3x = k/9 .........(1)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "P = 2x^2 = (k-7)/9................(2)\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting value of x from eqn 1 in 2<BR>\n" );
document.write( "2*(k/27)^2 = (k-7)/9<BR>\n" );
document.write( "18k^2 = 729(k-7)<BR>\n" );
document.write( "Transposing...<BR>\n" );
document.write( "18k^2 - 729k + 5103 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "Solving for k results in<BR>\n" );
document.write( "k = 315, 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );