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CGP EDU Academic Team
Published on: August 14, 2026
Let a,b,c ∈ R. If f(x) = ax 2 + bx + c is such that a + b + c = 3 and f(x + y) = f(x) + f(y) + xy, ∀ x,y ∈ R, then 
is equal to
Text Solution
Verified by ExpertsThe correct answer is:
A
Sol. f(x) = ax 2 + bx + c
f(x + y) = f(x) + f(y) + xy
a(x + y) 2 + b(x+ y) + c = ax 2 + bx + c + ay 2 + by + c + xy
2axy = c + xy ∀ x, y ∈ R
(2a – 1)xy – c = 0 ∀ x, y ∈ R
⇒ c = 0, a = 
a + b + c = 3
+ b + 0 = 3
b = 
∴ f(x) = 
x 2 + 
x
= 
⇒ 
= 330
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