The correct answer is Option (2) → an integer
Since f: Z → Z is given by
f(x)=ax2+bx+c for all x∈Z.
∴ f(x) = ax^2 + bx + c takes integral values for all x ∈ Z
⇒ f(x) is an integer for all x ∈ Z
⇒ f(0) and f(1) are integers.
⇒ f(1) - f(0) is an integer.
⇒ (a+b+c) -c is an integer [∵ f(0) = c and f(1) = a+b+c]
⇒ a+b is an integer. |