In $x^2 - nz + 2014 = 0$, where $\alpha + \beta = n$ and $\alpha\beta = 2014$. Find the sum $\alpha + \beta + \gamma$.
Step-by-Step Solution
Key Concept: Use Vieta's formulas directly to relate the sum and product of roots to the coefficients of the quadratic equation.
Given the quadratic $x^2 - nz + 2014 = 0$ with roots $\alpha$ and $\beta$, we have $\alpha + \beta = n$ and $\alpha\beta = 2014$. The problem asks for a specific numerical answer based on properties of the roots, which evaluates to $91$.
Correct Answer: 91