Question

If $f\left(x\right)=x^2-\lambda x+\mu$ be an integral function of the integral variable $x$ then

• A. $\lambda$ is an integer and $\mu$ is a rational fraction
• B. $\lambda$ and $\mu$ are integers
• C. $\mu$ is an integer and $\lambda$ is a rational fraction
• D. $\lambda$ and $\mu$ are rational fractions

Answer 1

The correct option is B $\lambda$ and $\mu$ are integers

Given that for all the integral values of $x$, $f\left(x\right)$ is an integer.
$x^2-\lambda x+\mu$ should be an integer.
$x^2$ is an integer since $x$ is an integer. For $-\lambda x+\mu$ to be an integer for all integral values of $x$, $\lambda$ and $\mu$ should be integers.