Hasse- Minkowski principle for Quadratic forms over Q

One of the main interesting topic in algebra is to find the roots of non-zero polynomials and writing down them explicitly over a given field K. The case which we consider in this project is the space of quadratic forms, which are homogeneous polynomials of degree 2, over Q. If they arise over Z, then we can study the zeros of these quadratic form by looking at them over Zp and study if that has zero in\ud Zp or not. By Hensels lemma, this studied over the reduction modulo p