Hi guys,

I'm having trouble proving that if

is transcendent, then

and

(where

is some non-zero rational constant) are transcendental.

I know that if

is algebraic, then it is the root of some polynomial,

. Then, if this is a linear polynomial in

, is it right to conclude that any roots will be in

? If that is the case, can we then set some other polynomial,

and conclude a contradiction?

For the other one, if we have

is algebraic, then it is the root of

. I don't know where to proceed from here, really.

Thank you in advance,

HTale.