Step 1: Identify the given quadratic equation and its roots. The quadratic equation is $x^2 - 4x + 2 = 0$. The roots are $\alpha$ and $\beta$. Step 2: Use Vieta's formulas to find the sum and product of the roots. 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 $c=2$. $$ \alpha + \beta = -\frac{-4}{1} = 4 $$ $$ \alpha \beta = \frac{2}{1} = 2 $$ Step 3: Simplify the expression $\frac{1}{\alpha} + \frac{1}{\beta}$. To add these fractions, find a common denominator: $$ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{\beta}{\alpha\beta} + \frac{\alpha}{\alpha\beta} = \frac{\alpha + \beta}{\alpha\beta} $$ Step 4: Substitute the values of $\alpha + \beta$ and $\alpha \beta$ into the simplified expression. $$ \frac{\alpha + \beta}{\alpha\beta} = \frac{4}{2} = 2 $$ The value of $\frac{1}{\alpha} + \frac{1}{\beta}$ is 2. The final answer is $\boxed{\text{2}}$.