Let f(x) be a cubic polynomial with f(1) = $$-$$10, f($$-$$1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x = $$-$$1. Then f(3) is equal to ____________.

If 'R' is the least value of 'a' such that the function f(x) = x² + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function f(x) = x² + ax + 1 is decreasing on [1, 2], then
the value of |R $$-$$ S| is ___________.

The number of distinct real roots of the equation 3x⁴ + 4x³ $$-$$ 12x² + 4 = 0 is _____________.