A Sufficient, Not Necessary Minimum

Let $f(x) = \left(x^2 + ax - a\right)e^{1-x}$, where $a \in \mathbb{R}$.

1. Find the number of zeros of $f'(x)$. 2. Prove that "$a \geqslant 0$" is a sufficient but not necessary condition for $f(x)$ to attain a minimum value on $\mathbb{R}$.