QJEEM17Ma1e13: JEE Main 2017 Mathematics - Class 11 JEEM17Ma1e13 Solution: Let a , b, c ∈ R . If f (x) = ax 2 + bx + c is such that a + b…

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

$$\sum _{n=1}^{10}f(n)$$ = 3 + 7 + 12 + 18 + 25 + 33 + 42 + 52 + 63 + 75 = 330