Question 250639
I think I understand what you are saying.
Let f(x) and g(x) be two polynomials with integer coefficients.
Since {{{a}}} was given to us as a zero,
{{{f(x)*a = g(x)}}}
multiply both sides by {{{a^(-1)}}} to get
{{{f(x) = g(x)*a^(-1)}}
Now it seems that {{{a^(-1)}}} is also algebraic since it is the zero for f(x).

Is that what you were needing?