Let a, b, c \in R. If f(x) = ax2 + bx + c is such that a + b + c = 3 and f(x + y) = f(x) + f(y) + xy, \forall x,y \in R, then \sum\limits_{n = 1}^{10} {f(n)} is equal to

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Answer: D. 330 f(x) = ax2 + bx + c f(1) = a + b + c = 3 \Rightarrow f (1) = 3 Now f(x + y) = f(x) + f(y) + xy ...(1) Put x = y = 1 in eqn (1) f(2) = f(1) + f(1) + 1 = 2f(1) + 1 \Rightarrow f(2) = 7 Similarly f(3) = 12 f(4) = 18 \sum\limits_{n = 1}^{10} {f(n)} = 3 + 7 + 12 + 18 + 25 + 33 + 42 + 52 + 63 + 75 = 330

Let $$a$$, b, c $$ \in R$$. If $$f$$(x) = ax2 + bx + c is such that $$a$$ + b + c = 3 and $$f$$(x + y) = $$f$$(x) + $$f$$(y) + xy, $$\forall x,y \in R,$$ then $$\sum\limits_{n = 1}^{10} {f(n)} $$ is equal to

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