Quadratic Equation and Inequalities Part 1

Let ƒ(x) = (c – 5) x2 – 2cx + c – 4
∴ ƒ(0)ƒ(2) < 0 .....(1)
& ƒ(2)ƒ(3) < 0 .....(2)
from (1) & (2)
(c – 4)(c – 24) < 0
& (c – 24)(4c – 49) < 0
⇒

49

4

< c < 24
∴ s = {13 , 14 , 15 , ... , 23}
Number of elements in set S = 11