Double roots of random littlewood polynomials

We consider random polynomials whose coefficients are independent and uniform on -1, 1. We prove that the probability that such a polynomial of degree n has a double root is o ( n -2 ) when n +1 is not divisible by 4 and asymptotic to 1/√(3) otherwise. This result is a corollary of a more general theorem that we prove concerning random polynomials with independent, identically distributed coefficients having a distribution which is supported on -1, 0, 1 and whose largest atom is strictly less than 8√(3)/πn^2 . In this general case, we prove that the probability of having a double root equals the probability that either -1, 0 or 1 are double roots up to an o ( n -2 ) factor and we find the asymptotics of the latter probability.