Identify the given quadratic equation and its roots.

The quadratic equation is $x^2 - 4x + 2 = 0$.
The roots are $\alpha$ and $\beta$.

For a quadratic equation $ax^2 + bx + c = 0$, the sum of the roots is $\alpha + \beta = -\frac{b}{a}$ and the product of the roots is $\alpha \beta = \frac{c}{a}$.
In this equation, $a=1$, $b=-4$, and $c=2$.

To add these fractions, find a common denominator:

The value of $\frac{1}{\alpha} + \frac{1}{\beta}$ is 2.

The final answer is $\text{2}$.