Take a fixed degree n polynomial. A very old and natural inquiry questions the localization of the roots of this polynomial, and its possible properties. Now, take all the coefficients of this polynomial random iid, say gaussian: Is there some special statistical properties of its zeroes? We will see that when the degree n is big, the local behavior of these points can be compared to a statistical physics model of positively charged particles (i.e. a Coulomb gas) and we will explore the theorems that are shown for this Coulomb gas and the associated conjectures for the zeroes of the random polynomial.