Question

Linear and Quadralic Equations and Inequalities.
Prove that if $a{x}^2+bx+cϵZforallxϵZthena,b,c,ϵZ.$

Answer 1

We know that the addition, subtraction and multiplication of two or more integers results in and integer.

Here, $a,b,c,x\in Z$

$⟹a{x}^2=a.x.x\in Z$

and $b.x\in Z$

and $c\in Z$

$⟹a{x}^2+bx+c\in Z$