Rational Number is Algebraic

Theorem
Let $r \in \Q$ be a rational number.

Then $r$ is also an algebraic number.

Proof
Let $r$ be expressed in the form:
 * $r = \dfrac p q$

Consider the linear polynomial in $x$:
 * $q x - p = 0$

which has the solution:
 * $x = \dfrac p q$

Hence the result, by definition of algebraic number.