If by rational zeros you mean values of x where f(x) goes to zero, there are none.
This is an equation of a parabola whose vertex is at (0, 2). f(x) never gets closer to 0 than that.
3 X^2 + 2 is a positive quantity for all values of X, there is no rationl number that makes a positive quantity 0.
The zeros of 3x^2 + 2 are the values of x that make the expression evaluate to zero.
Solve 3x^2 + 2 = 0.
Subtract 2 from both sides:
3x^2 = -2
x^2 = -2/3
|x| = i √(2/3)
x = ± i (√(6))/3
The zeros are complex (imaginary) numbers which are not rational. ("Rational" means a ratio (fraction) of integers.) NOT that it matters to the answer, but here even the coefficients of i are irrational.