Let $u$ be a root of the equation
$$
x^{3}-3 x+10=0
$$

Let $f(x)$ be a quadratic polynomial with rational coefficients, and
$$
\alpha=\frac{1}{2}\left(u^{2}+u-2\right), f(\alpha)=u .
$$

Find $f(0)$.
(2010, Five Schools Joint Examination for Independent Enrollment)