Any linear combination of $\{a_1,a_2,\cdots,a_n\}$ is also separable over $K$

Question

Let $E$ be a finite extension over $K$. If $E = K(a_1,a_2,\cdots,a_n)$ and each $a_i$ is separable over $K$ then can we say that any linear combination of $\{a_1,a_2,\cdots,a_n\}$ is also separable over $K$?

Answer 1

The set of separable elements over a field form a field in itself, and in particular linear combinations. See for example here.