document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=815591>Question 815591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^3 + (1 - k^2)x + k\r<BR>\n" );
document.write( "\n" );
document.write( "(a) Show that -k is a root of f.<BR>\n" );
document.write( "I've already solved this by substituting -k to the x's in the given equation. I'm not sure tho.\r<BR>\n" );
document.write( "\n" );
document.write( "(b) Find, in terms of k, the other roots of f.\r<BR>\n" );
document.write( "\n" );
document.write( "what I did is:\r<BR>\n" );
document.write( "\n" );
document.write( "let x + k a factor.<BR>\n" );
document.write( "divide the equation  x^3 + (1 - k^2)x + k by x + k<BR>\n" );
document.write( "then I got x^2 + kx + 1<BR>\n" );
document.write( "I then used quadratic formula to get the 2 other roots:\r<BR>\n" );
document.write( "\n" );
document.write( "x = -k + or - square root of (k^2 - 4) <BR>\n" );
document.write( "    __________________________________<BR>\n" );
document.write( "                   2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(c)Find the set of values of k for which f has exactly one real root. \r<BR>\n" );
document.write( "\n" );
document.write( "? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491081 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=491081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Everything you've done is correct. All that is left is part c. A quadratic has exactly one real root when the expression inside the square root is a zero. So all you have to do is figure out when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2-4 ALIGN=MIDDLE  ALT=\"k%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is zero. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );