JEE Main 2019 Mathematics question
Consider the quadratic equation , c ≠ 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:
Answer: (D)
Solution
f(0)f(2) < 0 and f(2)f(3) < 0: (c − 4)(c − 24) < 0 and (c − 24)(4c − 49) < 0 ⇒ 12.25 < c < 24: c = 13, …, 23.