Question 529811
Any rational zero can be found through this equation


*[Tex \LARGE Roots=\frac{p}{q}] where p and q are the factors of the last and first coefficients



So let's list the factors of 91 (the last coefficient):


*[Tex \LARGE p=\pm1, \pm7, \pm13, \pm91]


Now let's list the factors of 7 (the first coefficient):


*[Tex \LARGE q=\pm1, \pm7]


Now let's divide each factor of the last coefficient by each factor of the first coefficient



*[Tex \LARGE \frac{1}{1}, \frac{1}{7}, \frac{7}{1}, \frac{7}{7}, \frac{13}{1}, \frac{13}{7}, \frac{91}{1}, \frac{91}{7}, \frac{-1}{1}, \frac{-1}{7}, \frac{-7}{1}, \frac{-7}{7}, \frac{-13}{1}, \frac{-13}{7}, \frac{-91}{1}, \frac{-91}{7}]







Now simplify


These are all the distinct rational zeros of the function that could occur


*[Tex \LARGE  1, \frac{1}{7}, 7, 13, \frac{13}{7}, 91, -1, -\frac{1}{7}, -7, -13, -\frac{13}{7}, -91]



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