Question
Let a, b, c ∈ R. If f(x) = ax^{2} + bx + c is such
that a + b + c = 3 and f(x + y) = f(x) + f(y) + xy, ∀x,y ∈ R,then is equal to

225

330

165

190
Solution
B.
330
f(x) = ax^{2} + bx + c
f(1) = a + b + c = 3
Now f(x + y) = f(x) + f(y) + xy
put y = 1
f(x + 1) = f(x) + f(1) + x
f(x + 1) = f(x) + x + 3
Now
f(2) = 7
f(3) = 12
Now
Sn = 3 + 7 + 12 + ..... t^{n} ...(1)
Sn = 3 + 7 + ......t^{n – 1} + t^{n} ...(2)
On subtracting (2) from (1)
tn = 3 + 4 + 5 + ....... upto n terms