![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
.
\n" ); document.write( "Determine the set of values of the constant k for which the line y = 4x + k does not
\n" ); document.write( "intersect the curve y = x^2
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Here an Algebra solution is placed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "If the/an intersection point does exist, then an equation\r\n" );
document.write( "\r\n" );
document.write( " x^2 = 4x + k (1)\r\n" );
document.write( "\r\n" );
document.write( "has a real solution. This equation is equivalent to\r\n" );
document.write( "\r\n" );
document.write( " x^2 - 4x - k = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The discriminant of this quadratic equation is\r\n" );
document.write( "\r\n" );
document.write( " d = b^2 - 4ac = (-4)^2 - 4*1*(-k) = 16 + 4k.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The discriminant is positive if and only if\r\n" );
document.write( "\r\n" );
document.write( " 16 + 4k >= 0\r\n" );
document.write( "\r\n" );
document.write( " 4k >= -16\r\n" );
document.write( "\r\n" );
document.write( " k >= -16/4 = -4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus a real solution to equation (1) does exists if and only if k >= -4.\r\n" );
document.write( "\r\n" );
document.write( "If k < -4, there is no real solution for equation (1), so the intersection does not exist.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER. The set of values of \"k\" is { k < -4 }.\r\n" );
document.write( "\r\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "