Solution
= Solution
A <splitting field> of $f\in K[X]$ is an extension $L/K$ in which
$$
f(X)=c\prod_{r=1}^d(X-\alpha_r)
$$
for roots $\alpha_r\in L$, and which is generated by those roots:
$$
\boxed{L=K(\alpha_1,\ldots,\alpha_d)}.
$$
The generation condition is the required minimality: no proper intermediate field containing $K$ can still contain every root.