Question 229700
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The rational root theorem says that a constraint on rational solutions (or roots) of the polynomial equation


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a_nx^n\ +\ a_{n-1}x^{n-1}\ +\ \cdots\ +\ a_0]


with integer coefficients is: If *[tex \LARGE a_n] and *[tex \LARGE a_0] are non-zero, then each rational solution *[tex \LARGE x] when written as a fraction, *[tex \LARGE x\ =\ \pm\frac{p}{q}] in lowest terms satisfies:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ p] is an integer factor of the constant term *[tex \LARGE a_0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ q] is an integer factor of the leading coefficent *[tex \LARGE a_n]


For your problem, *[tex \LARGE p] must be an integer factor of 2, so list all of those, and *[tex \LARGE q] must be an integer factor of 3, so list those.  Remember that 1 is an integer factor of any integer.  Now, create all possible fractions of the form *[tex \LARGE \pm\frac{p}{q}], which is the list of possible rational roots.  Remember, not all of the possibles will actually be roots, the theorem only says that IF a rational number is a root, THEN it has that form.  The converse of the theorem statement is not necessarily true. 


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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