Find the set of possible rational zeros of the given function.
\[
f(x)=4 x^{4}-10 x^{2}+x+6
\]

Step 1 ：The Rational Root Theorem states that if a polynomial has a rational root, then it must be a factor of the constant term divided by a factor of the leading coefficient. In this case, the constant term is 6 and the leading coefficient is 4. So, the possible rational roots are factors of \(\frac{6}{4}\), or \(\frac{3}{2}\). The factors of \(\frac{3}{2}\) are ±1, ±\(\frac{1}{2}\), ±3, ±\(\frac{3}{2}\).

Step 2 ：The roots of the function are complex numbers, not rational numbers. Therefore, there are no rational roots for the given function.

Step 3 ：Final Answer: The set of possible rational zeros of the given function is \(\boxed{\emptyset}\).