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JEE Advanced Mathematics Application of Derivatives 2024 JEE Advanced 2024 (Paper 2)

JEE Advanced Mathematics Question (2024) — Solution

Question

Let the function f: R R be defined by f(x)= x e^ x (x^ 2023 +2024 x+2025 ) (x^2-x+3 ) + 2 e^ x (x^ 2023 +2024 x+2025 ) (x^2-x+3 ) . Then the number of solutions of f(x)=0 in R is

Options

  1. A. A
  2. B. B
  3. C. C
  4. D. D

Answer

A. A

Step-by-step solution

f(x)= (x^ 2023 +2024 x+2025 ) e^ x (x^2-x+3 ) ( x+2) ( x+2) is never zero for x^ 2023 +2024 x+2025=0 aligned & let ( x )= x ^ 2023 +2024 x +2025 \\ & ^ ( x )=2023 x ^ 2022 +2024>0 x R aligned ( x ) is an Strictly Increasing function ( x )=0 for exactly one value of x f ( x )=0 has one solution

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