Solve the equation

Question:

Let $a, b, c \in R$. If $f(x)=a x^{2}+b x+c$ is such that $a+b+c=3$ and $f(x+y)=f(x)+f(y)+$ $x y, \forall x, y \in R$, then $\sum_{n=1}^{10} f(n)$ is equal to :

  1. 255

  2. 330

  3. 165

  4. 190


Correct Option:

Solution:

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