I read a proof of the transcendence of $ pi $ but I'm stuck with a problem about polynomials. The proof begins like this:

"Suppose $ { beta _1}, { beta _2}, ldots, { beta _n} $ are the roots of an equation

$ d {x ^ m} + {d_1} {x ^ {m – 1}} + ldots + {d_m} = 0 $

with integral coefficients. Any symmetrical integral polynomial in

$ {d beta _1}, {d beta _2}, dots, {d beta _n} $

is an integer. "

Can any one explain it please?