14. List the potential rational zeros for the polynomial: \( f(x)=10 x^{4}-x^{2}+25 \)

To discover potential rational zeros for the polynomial \( f(x) = 10x^4 - x^2 + 25 \), we can use the Rational Root Theorem, which suggests that any rational solution \( \frac{p}{q} \) (where \( p \) is a factor of the constant term, and \( q \) is a factor of the leading coefficient) should be explored. Here, the constant term is \( 25 \) (factors are \( \pm 1, \pm 5, \pm 25 \)), and the leading coefficient is \( 10 \) (factors are \( \pm 1, \pm 2, \pm 5, \pm 10 \)). Therefore, the potential rational zeros are: \[ \text{Potential rational zeros: } \pm 1, \pm 5, \pm 25, \pm \frac{1}{1}, \pm \frac{1}{2}, \pm \frac{5}{2}, \pm \frac{5}{5}, \pm \frac{25}{1}, \pm \frac{25}{2}, \pm \frac{25}{5}, \pm \frac{25}{10} \] In simpler terms, that's \( \pm 1, \pm 5, \pm 25, \pm \frac{1}{2}, \pm \frac{5}{2}, \pm \frac{25}{2}, \pm \frac{5}{10}, \pm \frac{5}{5}, \pm \frac{25}{10} \). Now you've got a fun little list to work with! Happy zero hunting!