Q1 JEE Advanced 2025 Mathematics Paper 1 Solutions @qubitpune

Problem Statement : Let ℝ denote the set of all real numbers. Let 𝑎𝑖,𝑏𝑖∈ℝ for 𝑖∈{1,2,3}.
Define the functions 𝑓:ℝ→ℝ,𝑔:ℝ→ℝ, and ℎ:ℝ→ℝ by
𝑓(𝑥)=𝑎1+10𝑥+ 𝑎2𝑥2+𝑎3𝑥3+𝑥4, 𝑔(𝑥)=𝑏1+3𝑥+ 𝑏2𝑥2+𝑏3𝑥3+𝑥4, ℎ(𝑥)=𝑓(𝑥+1)−𝑔(𝑥+2).
If 𝑓(𝑥)≠𝑔(𝑥) for every 𝑥∈ ℝ, th