according to the rational root theorem, what are all the potential rational roots of f(x) = 9x^4 - 2x^2 - 3x…

Explanation:

Step1: Identify leading - coefficient and constant

For the polynomial $f(x)=9x^{4}-2x^{2}-3x + 4$, the leading - coefficient $a_{n}=9$ and the constant term $a_{0}=4$.

Step2: Find factors of leading - coefficient and constant

The factors of $a_{n}=9$ are $\pm1,\pm3,\pm9$. The factors of $a_{0}=4$ are $\pm1,\pm2,\pm4$.

Step3: Apply Rational Root Theorem

The potential rational roots are of the form $\frac{p}{q}$, where $p$ is a factor of $a_{0}$ and $q$ is a factor of $a_{n}$. So the potential rational roots are $\pm\frac{1}{9},\pm\frac{2}{9},\pm\frac{1}{3},\pm\frac{4}{9},\pm\frac{2}{3},\pm1,\pm\frac{4}{3},\pm2,\pm4$.

Answer:

$\pm\frac{1}{9},\pm\frac{2}{9},\pm\frac{1}{3},\pm\frac{4}{9},\pm\frac{2}{3},\pm1,\pm\frac{4}{3},\pm2,\pm4$