Which statement about the polynomial function g(x) is true?

If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.
If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.