I am having problem doing this problem it is asking to find the condition that must be satisfied by k in order that the expression may be positive for all real values of x.
Can some help me with this problem?
That's a parabola , so it'll be always positive iff (1) it is a "smiling" or convex upwards parabola (i.e., its higher coefficient is positive), and (2) its discriminant is negative, i.e.: iff it has no real roots, so:
:
Taking together both conditions for k on (1)-(2) the solution is immediate.
Tonio