List all potential rational zeros. $$ f(x)=x^{5}-3 x^{2}+7 $$

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1. The given polynomial is 
   $$
   f(x) = x^5 - 3x^2 + 7.
   $$

2. The Rational Root Theorem states that any possible rational zero of a polynomial with integer coefficients is of the form 
   $$
   \frac{p}{q},
   $$
   where $$ p $$ is a divisor of the constant term and $$ q $$ is a divisor of the leading coefficient.

3. For $$ f(x) $$:
   - The constant term is $$ 7 $$.
   - The leading coefficient is $$ 1 $$.

4. The divisors of $$ 7 $$ (the constant term) are:
   $$
   \pm 1, \pm 7.
   $$

5. The divisors of $$ 1 $$ (the leading coefficient) are:
   $$
   \pm 1.
   $$

6. Therefore, the possible rational zeros are:
   $$
   \frac{p}{q} = \pm 1, \pm 7.
   $$

Thus, the list of all potential rational zeros is 
$$
\pm 1, \pm 7.
$$
The potential rational zeros are $$ \pm1 $$ and $$ \pm7 $$.

List all potential rational zeros.

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