document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=865629>Question 865629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One of the roots of the equation y= -2x^2+kx+(k+2) is located at x=3<BR>\n" );
document.write( "A) determine the value of k<BR>\n" );
document.write( "B) determine the other root of this equation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521797 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=521797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One of the roots of the equation y= -2x^2+kx+(k+2) is located at x=3<BR>\n" );
document.write( "A) determine the value of k<BR>\n" );
document.write( "B) determine the other root of this equation\r<BR>\n" );
document.write( "\n" );
document.write( "To determine k, we substitute x=3 into the equation -2x^2 + kx + (k+2) = 0<BR>\n" );
document.write( "This gives -2(3)^2 + 3k + k + 2 = 0<BR>\n" );
document.write( "Solving for k gives k=4<BR>\n" );
document.write( "So the equation is y = -2x^2 + 4x + 6<BR>\n" );
document.write( "To get the other root, we know that one of the factors of this quadratic is x-3.<BR>\n" );
document.write( "From this we can determine the other factor:<BR>\n" );
document.write( "(x-3)(-2x-2) = 0<BR>\n" );
document.write( "This gives x=-1\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );