  We are interested in irrationality of roots for seven important families of
polynomials : Tchebichef polynomials, Legendre polynomials, Laguerre
polynomials, Hermite polynomials, Bessel polynomials, Bernoulli polynomials and
Euler polynomials. One first proves, for the most part of them, existence of
real roots then one studies the irrationality of them. The methods used are
based on elementary arithmetical properties of algebraic numbers, some of them
becoming from more general proofs that have allowed to derive the
irreducibility of some of these polynomials.
