Question 97
Let $n$ be a positive integer. Prove that all roots of the equation
$$
x(x+2)(x+4) \ldots(x+2n) + (x+1)(x+3) \ldots(x+2n-1) = 0
$$
are real and irrational.
$$
x(x+2)(x+4) \ldots(x+2n) + (x+1)(x+3) \ldots(x+2n-1) = 0
$$
are real and irrational.