Find all the zeros. Write the answer in exact form. \[ q(x)=2 x^{4}-7 x^{3}+3 x^{2}+8 x-4 \] If there is more than one answer, separate them with commas. Select "None" if applicable. The rational zeros of \( q(x): \)

To find the rational zeros of the polynomial \( q(x) = 2x^4 - 7x^3 + 3x^2 + 8x - 4 \), we can use the Rational Root Theorem. The possible rational zeros are given by the factors of the constant term (-4) divided by the factors of the leading coefficient (2). Thus, the candidates are \( \pm 1, \pm 2, \pm 4, \pm \frac{1}{2}, \pm \frac{2}{2}, \pm \frac{4}{2} \), leading to possible rational zeros: \( \pm 1, \pm 2, \pm 4, \pm \frac{1}{2} \). After testing these values using synthetic or polynomial division, you'll find that \( x = 2 \) and \( x = \frac{1}{2} \) are indeed zeros. We can then factor \( q(x) \) using these roots. After factoring, we can determine that the complete list of rational zeros for the polynomial \( q(x) \) includes: \( 2, \frac{1}{2} \).