Verified Solution • 2025–26 Session moderate

QJEEM24Mae7d5: JEE Main 2024 Mathematics - Class 11 JEEM24Mae7d5 Solution: Let S be the set of positive integral values of a for which a x …

Let S be the set of positive integral values of a for which ax2+2(a+1)x+9a+4x2−8x+32<0,∀x∈R. Then, the number of elements in S is :

Multiple Choice Options

  • A 0
  • B ∞
  • C 3
  • D 1

Step-by-Step Verified Solution

x^2-8 x+32&gt;0 \forall x \in R as discriminant of this quadratic is 64-4 \times 32&lt;0

⇒ax2+2(a+1)x+9a+4<0∀x∈R

⇒\Rightarrow Only possible when a&lt;0 and D&lt;0

⇒\Rightarrow Since SS is set of positive values of a⇒Sa \Rightarrow S is a null set

⇒n(S)=0

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