Using the rational root test (subject Math GRE exam 9768 Q.31)

Question

I used the rational root test and my answer was B as -5 does not divide 9, but the correct answer is C. Could anyone clarify this for me please?

Answer 1

By Rational Root theorem, if $\frac{p}{q}$ is a root(in lowest terms) then $p \mid b$ and $q \mid 9$ provided $b \neq 0$.

As $4 \nmid 9$, therefore $\frac 14$ cannot be a root.

Answer 2

The rational roots must be of the form

$$\dfrac{\text{divisor of b}}{\text{divisor of 9}}$$

The only number not of this form is $\frac 14$.