Question 3 - Set of roots of polynomials

Let P be the set of all polynomials of the form m x2 + 2 (m - 4) x + m2 - 1 where m is an integer in the range [-100, 100]. Define the set

So S is the set of all roots to polynomials from P. For example, 6 is a root of x2 - 6 x, obtained for m=1, so 6 ϵ S.

1. Determine the number of elements of S. Note that since S is a set, duplicate elements should not be counted.

2. Determine the number of elements of S that are real numbers.