Proposition
Let $ K(\alpha)/K $ be a finite simple extension, with $ f \in K[X] $ the minimal polynomial for $ \alpha$. Given a field extension $ \theta : K \to L $, the number of embeddings $ \tilde{\theta} : K(\alpha) \to L $ extending $ \theta$ is precisely the number of distinct roots of $ \theta(f) $ in $L$
The proof I have of this proceeds by stating that "An embedding $K(\alpha) \to L $ extending $\theta$ must send $\alpha$ to a zero of $\theta(f)$"
I just can't see why this is true. Any help would be greatly appreciated.