Case – 1

c – 5 > 0 ………….(i)

f (0) > 0

c – 4 > 0 ……………(ii)

f (2)< 0

4(c – 5) – 4c + c – 4 < 0

c < 24 ………..(iii)

f (2) > 0

9(c) –5) – 6c – c – 4 > 0

$4\mathrm{C}-49>0\Rightarrow \mathrm{C}>\frac{49}{4}$  ………(iv)

 Here (i) $\cap$(ii) $\cap$ (iii) $\cap$(iv)

$\mathrm{C}\in (\frac{49}{4},24)$

Case – II

c – 5 < 0 …………….(i)

f (0) < 0

c < 4 ……………..(ii)

f (2) > 0⇒c > 24 ………..(iii)

f (3) < 0⇒c < 49 ………..(iv)

4 ⇒ c$\in$f

$\mathrm{c}\in (\frac{49}{4},24)$