Verified Solution • 2025–26 Session moderate

QJEEM19Ma0f96: JEE Main 2019 Mathematics - Class 11 JEEM19Ma0f96 Solution: Consider the quadratic equation (c – 5)x 2 – 2cx + (c – 4) = 0, …

Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, 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 -

Multiple Choice Options

  • A 12
  • B 18
  • C 10
  • D 11

Step-by-Step Verified Solution

JEE Main 2019 (Online) 10th January Morning Slot Mathematics - Quadratic Equation and Inequalities Question 130 English Explanation

Let f(x) = (c − 5)x2 − 2cx + c − 4

∴  f(0)f(2) < 0      . . . . .(1)

& f(2)f(3) < 0      . . . . .(2)

from (1) and (2)

(c − 4)(c − 24) < 0

& (c − 24)(4c − 49) < 0

⇒  494 < c < 24

∴  s = {113, 14, 15, . . . . . 23}

Number of elements in set S = 11

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