Let \mathbb{R} denote the set of all real numbers. Let a_i, b_i \in \mathbb{R} for i \in\{1,2,3\}. Define the functions f: \mathbb{R} \rightarrow \mathbb{R}, g: \mathbb{R} \rightarrow \mathbb{R}, and h: \mathbb{R} \rightarrow \mathbb{R} by f(x)=a_1+10 x+a_2 x^2+a_3 x^3+x^4 g(x)=b_1+3 x+b_2 x^2+b_3 x^3+x^4 h(x)=f(x+1)-g(x+2) If f(x) \neq g(x) for every x \in \mathbb{R}, then the coefficient of x^3 in h(x) is [JEE Adv 2025 P1]

Quadratic Equation and Inequalities

Section: Mathematics

Question : 1 of 23

Marks: +1, -0

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, then the coefficient of x3 in h(x) is

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