abstract algebra - Linearly disjoint?

Let $f$ and $g$ be irreducible polynomials over a field $K$ with $\deg f=\deg g =3$ and let the discriminant of $f$ be positive and the discriminant of $g$ negative.

Does it follow that the splitting fields of $f$ and $g$ are linearly disjoint? If yes, why?

(Def.: Two intermediate fields $M_1, M_2$ of an algebraic field extension $L|K$ are called linearly disjoint, if every set of elements of $M_1$, that is linearly independent over $K$, is also linearly independent over $M_2$.
Here, this is equivalent to $M_1 \cap M_2 = K.$)