When an expression x² + 2kx + k² - 5k + 7 is always positive for all real values of x, its output value can never be zero. This is because zero is a non-positive figure.

In other words, there cannot be any real roots (solution) to the equation x² + 2kx + k² - 5k + 7 = 0.

[Graphically, this means that the curve y = x² + 2kx + k² - 5k + 7 will always lie above the x-axis and will never touch or cut the x-axis at all]

So, the discriminant of roots will be negative.

Discriminant < 0

But what is our discriminant? It's (2k)² - 4 (1) (k² - 5k + 7), or simply 20k - 28.

So, 20k - 28 < 0
20k < 28
k < 1.4