Let a, b, c R. If f (x) = ax² + bx + c is such that a + b + c = 3 and f (x + y) = f (x) + f (y) + xy, x,y R, then Σ n = 1 ¹⁰ f(n) is equal to

Sets, Relations and Functions: JEE Main 2017 Mathematics question

JEE Main 2017 · Session, Shift 1 · Q3859

JEE Main 2017Session, Shift 1MathematicsEasySets, Relations and Functions168× since 2002

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