Let $\mathrm{\Phi }$ be an irreducible (possibly noncrystallographic) root system of rank $l$ of type P. For the corresponding cluster complex $\mathrm{\Delta }(P)$, which is known as pure $(l-1)$-dimensional simplicial complex, we define the generating function of the number of faces of $\mathrm{\Delta }(P)$ 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 ${\mathrm{\Delta }}_{+}(P)$ of the complex $\mathrm{\Delta }(P)$ 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.