Let $\Phi$ be an irreducible (possibly noncrystallographic) root system of rank $l$ of type P. For the corresponding cluster complex $\Delta(P)$, which is known as pure $(l − 1)$-dimensional simplicial complex, we define the generating function of the number of faces of $\Delta(P)$ with dimension $i − 1$, which is called $f$-polynomial. We show that the $f$-polynomial has exactly $l$ simple real zeros on the interval $(0, 1)$ and the smallest root for the infinite series of type $A_l , B_l$, and $D_l$ monotone decreasingly converges to zero as the rank $l$ tends to infinity. We also consider the generating function (called the $f^+$-polynomial) of the number of faces of the positive part $\Delta_+(P)$ of the complex $\Delta(P)$ with dimension $i − 1$, whose zeros are real and simple and are located in the interval $(0, 1)$, including a simple root at $t = 1$. We show that the roots in decreasing order of $f$-polynomial alternate with the roots in decreasing order of $f^+$-polynomial.