calculus – If $f”(x)−f'(x)−f(x)−1=0$ and $f(0)=f(k)=0$ what can we say about values that $f(x)$ takes over $(0,k)$?

Here $f(x)$ a twice-differentiable function that solves the differential equation $f”(x)−f'(x)−f(x)−1=0$ over $R$ and satisfies the condition $f(0) = 0 = f(k)$ for some $k > 0$. Does $f(x)$ take both positive and negative values over $(0,k)$ or does it take only positive or only negative values over this interval?