Answer: k < 2 or k > 6.
Step-by-step explanation:
2x - k = xˆ2 + kx - 2
xˆ2 + (k - 2)x + (2 - k) = 0
For the line to meet the curve at two distinct points, this quadratic equation must have two distinct real roots. In other words, the discriminant (bˆ2 - 4ac) must be greater than zero:
(k - 2)ˆ2 - 4(2 - k) > 0
kˆ2 - 8k + 12 > 0
(k - 6)(k - 2) > 0
This inequality is satisfied when k < 2 or k > 6. Therefore, the set of values of k for which the line y= 2x-k meets the curve y= xˆ2+kx-2 at two distinct points is k < 2 or k > 6.