Consider the quadratic equation (c – 5)x 2 – 2cx + (c – 4) = 0, c ¹ 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is:

Consider the quadratic equation $(c-5) x^{2}-2 c x+(c-4)=0$, $\mathrm{c} \neq 5$. Let $\mathrm{S}$ be the set of all integral values of $\mathrm{c}$ for which one root of the equation lies in the interval $(0,2)$ and its other root lies in the interval $(2,3)$. Then the number of elements in $\mathrm{S}$ is: