1. The problem statement, all variables and given/known data Let α be a transcendental number and β an algebraic number. Prove that α+β is transcendental. 3. 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. So, p(x)= b+b1x1+b2x2+b3x3+...+b(n-1)xn-1+bnxn I'm stuck, I'm not sure where to go from here... Any help is appreciated. Thanks.