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If x^2 + ax + b is an integer for every integer x then

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If x2 + ax + b is an integer for every integer x then 

(A)  a is always an integer but b need not be an integer. 

(B)  b is always an integer but a need not be an integer.

(C)  a + b is always an integer.

(D)  a and b are always integers.

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1 Answer

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Correct option  (C), (D)

Let f(x) = x2 + ax + b

Clearly, f(0) = b ⇒ b is an integer.

Now, f(1) = 1 + a + b ⇒ a is an integer.

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