Consider the set $\mathbb{R}[X]$ of polynomials in $X$ with real coefficients as a real vector space. Let $T$ be the $\mathbb{R}$-linear operator on $\mathbb{R}[X]$ given by
$$T(f) = \frac{\mathrm{d}^{2}f}{\mathrm{d}X^{2}} - \frac{\mathrm{d}f}{\mathrm{d}X} + f$$
What is the nullity of $T$?