Question

Let $a,b,c$ be rational numbers and $f:Z\to Z$ be a function given by
$f\left(x\right)=a{x}^2+bx+c$ then $a+b$ is

• A. An integer
• B. A rational number but not an integer
• C. Negative integer
• D. Nothing in particular can be said

Answer 1

The correct option is A An integer

$f:Z\to Z$ is given by
$f\left(x\right)=a{x}^2+bx+c\forall x\in Z$
Now $f\left(0\right),f\left(1\right)$ are integers
$\Rightarrow f\left(1\right)-f\left(0\right)$ is integer
$\Rightarrow (a+b+c)-c$ is integer
$\Rightarrow a+b$ is an integer