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

Maths Quadratic Equations Solution of Quadratic Inequations and Miscellaneous Equations Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

‘a’ is always an integer but ‘b’ need not be an integer

‘b’ is always an integer but ‘a’ need not be an integer

a and b are always integers.

None of these

Text Solution

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The correct answer is:

Let f(x) = x 2 + ax + b

Clearly, f(0) = b ⇒ ⇒ b is an integer.

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

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