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?
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2 Answers
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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.
answered Jul 29, 2017 at 17:59
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$\begingroup$ and the GRE has successfully tested if you know the rational root test. $\endgroup$ Jul 29, 2017 at 18:07
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$\begingroup$ Wrong. Correct is: $ $ if $\,p/q\,$ is a root in lowest terms (i.e. $p,q$ coprime) then.... $\endgroup$ Jul 29, 2017 at 19:18
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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 $\frac 14$.
answered Jul 31, 2017 at 15:32
-5 does not divide 9That's not what the rational root test says. $\,-5 = \cfrac{-5}{1}\,$ where $1 \mid 9\,$, and $5$ could divide $b$. $\endgroup$