document.write( "Question 1177934: Given y = −3x^2 + kx − 12 for k > 0, find the value(s) of k such that y < 0 for all x. \n" ); document.write( "

Algebra.Com's Answer #807102 by ikleyn(52848) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "You are given that the quadratic function is always negative, for all values of x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that it has no real roots.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In turn, it means that the discriminant of this quadratic function is negative.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The discriminant of a quadratic function  y = ax^2 + bx + c is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    d = b^2 - 4ac.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In your case a= -3,  b= k,  c= -12,  so the discriminant is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    d = k^2 - 4*(-3)*(-12) = k^2 - 144.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You should determine \"k\" from this condition\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    d < 0,   or  k^2 - 144 < 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The solution is  k^2 < 144,   or   -12 < k < 12.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The values of \"k\"  are   -12 < k < 12.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );