The rational root theorem is used to determine the possible roots of a polynomial.
The possible roots are [tex]\mathbf{\pm \frac{1}{3}, \pm 3, \pm \frac{1}{2}}[/tex]
The function is given as:
[tex]\mathbf{f(x) = 9x^3 + 14x^2 - x + 18}[/tex]
The constant term in the above function is 18.
The factors of 18 are:
[tex]\mathbf{18 \to \pm1, \pm2, \pm3, \pm6, \pm9, \pm18}[/tex]
The lead coefficient in the above function is 9.
The factors of 9 are:
[tex]\mathbf{9 \to \pm1, \pm2, \pm3, \pm9}[/tex]
The possible rational roots are:
[tex]\mathbf{r = \frac{ \pm1, \pm2, \pm3, \pm6, \pm9, \pm18}{ \pm1, \pm2, \pm3, \pm6, \pm9}}[/tex]
The possible roots that can be gotten from the above expression are:
[tex]\mathbf{r = \pm \frac{1}{3}, \pm 3, \pm \frac{1}{2}}[/tex]
Hence, (a), (b), (d) are true
Read more about rational root theorem at:
https://brainly.com/question/16863333
