2. For a given positive integer k, a quadratic polynomial with bounded integer coefficients has the form P(x) = ax + bx + c, where a, b, c are integers in the range [-k, k]. There are 2k(2k + 1) of these - note that a cannot be 0. Show that there are k(3k + 1) of these polynomials which have 1 as a root, that is, with P(1) = 0