Let L be the splitting field of $ x^3- 2$ over $ \mathbb{Q}$. Then $ G=\operatorname{Gal}(L/K) \cong S_3$. Let $\sigma\in G$ such that the fixed field of $ \sigma$ is $\mathbb{Q}(2^{1/3})$. Let $x,y\in L $ be $Q $ independent and $x/y \in Q(2^{1/3}\omega)$ then can we always find a $\lambda\in \mathbb{Q}$ such that the expression $$ (y\sigma(y))\lambda^2 + (y\sigma(x) + x \sigma(y))\lambda + x\sigma(x)\in \mathbb{Q}.$$