If x2 + ax + b is an integraleger for every integraleger x t... | MATH - SOLUTION OF QUADRATIC EQUATIONS AND NATURE OF ROOTS | SolveeIt | Solveeit

Today, August 19

Question

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 and b are always integers.

D

None of these

Answer

a and b are always integers.

Explanation

Solution

Let f(x) = x² + ax + b

Clearly, f(0) = b ⇒ b is an integer.

Now f(1) = 1+ a + b ⇒ a is an integer