Let α be a transcendental number and β an algebraic number. Prove that α+β is transcendental.
The Attempt at a Solution
It's known that adding two algebraic numbers results in an algebraic number.
Since β is algebraic, it is a root of a polynomial with integer coefficients.
That is p(x)=Ʃbix^i i=0 to n, p(β)=0.
I'm stuck, I'm not sure where to go from here...
Any help is appreciated.