Solution:
we have been asked to find the potential roots of the function
![f(x) = 5x^3-7x + 11](https://img.qammunity.org/2019/formulas/mathematics/middle-school/fqs7zc9qavskupk5ag45upl0hkb5qp7ugo.png)
using rational root theorem.
Here the constant term is 11 with factors 1 and 11 and the leading coefficients is 5 with factors 1 and 5.
So the potential roots of the given function as per the rational root theorem is
![\pm(1,11)/(1,5) =\pm(1)/(1,5) ,\pm(11)/(1,5)=\pm(1)/(1) ,\pm(11)/(1)\pm(1)/(5) ,\pm(11)/(5)\\\\\\\text{Hence the potential roots are }\\\\\pm1,\pm11,\pm(1)/(5),\pm(11)/(5)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/doujicebz9mrgn2efggx9ye4qzp5dk003c.png)