Question 1200188
.
Determine the set of values of the constant k for which the line y = 4x + k does not
intersect the curve y = x^2
~~~~~~~~~~~~~~~~~



            Here an Algebra solution is placed.



<pre>
If the/an intersection point does exist, then an equation

    x^2 = 4x + k     (1)

has a real solution.  This equation is equivalent to

    x^2 - 4x - k = 0.


The discriminant of this quadratic equation is

    d = b^2 - 4ac = (-4)^2 - 4*1*(-k) = 16 + 4k.


The discriminant is positive if and only if

    16 + 4k >= 0

    4k >= -16

     k >= -16/4 = -4.


Thus a real solution to equation (1) does exists if and only if k >= -4.

If k < -4, there is no real solution for equation (1), so the intersection does not exist.


<U>ANSWER</U>.  The set of values of "k" is  { k < -4 }.
</pre>

Solved.