FunctionHard
Question
Let f(x) = a x2 + b x + c, where a, b, c are rational and f : Z → Z, where Z is the set of integers. Then a + b is :
Options
A.a negative integer
B.an integer
C.non-integral rational number
D.none of these
Solution
f(x) = ax2 + bx + c
f(0) = c ⇒ c ∈ I
f(1) = a + b + c ⇒ (a + b + c) ∈ I
⇒ (a + b) ∈ I
f(0) = c ⇒ c ∈ I
f(1) = a + b + c ⇒ (a + b + c) ∈ I
⇒ (a + b) ∈ I
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