JEE Main 2017 Maths Question-Let a,b,c,\epsilon \: R if f\left ( x \right )= ax^{2}+bx+c is such

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Let a,b,c,\epsilon \: R if f\left ( x \right )= ax^{2}+bx+c is such that a+b+c=3 and

f(x+y)= f(x)+f(y)+xy \forall \: x,y\: \epsilon \: R\: then

\sum_{n=1}^{10}\: f(n) is equal to :

Option 1) 165
Option 2) 190
Option 3) 255
Option 4) 330