I want to show that every number field of degree $3$ is of the form $\mathbb{Q}(\alpha)$ where the minimal polynomial of $\alpha$ is of the form $m_\alpha(x) = x^3 + ax + b$.
Let $K$ be the cubic number field. By the primitive element theorem, we know $K = \mathbb{Q}(\beta)$ where $m_\beta(x) = x^3 + c_2x^2 + c_1x + c_0$. But I don't know how we can pick $\beta$ such that $c_2 = 0$.
Hints would be appreciated and thanks in advance.