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
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
A. A
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
Related: Mathematics — Application of Derivatives · All PYQ Banks