UPSEE Solved Model Paper 7

Given
f : Z → Z such that
f (x) = ax2 + bx + c, where a, b, c ∊ Q
We have to find the value of a + b
Now,
For x = 0 , f (0) = c = integer [Since f (0) ∊ Z because f ： Z → Z]
⇒ c is an integer
For x = 1, f (1) = a + b + c = k (say ) [where f (1) = k ∊ Z]
⇒ a + b = k - c ... (i)
Since k ∊ c , c ∊ Z ⇒ k - c ∊ Z
⇒ a + b ∊ Z [Using (i)]
⇒ a + b is an integer
Hence, option 'B' is correct