Solution:
we have been asked to find the potential roots of the function
[tex]f(x) = 5x^3-7x + 11[/tex]
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
[tex]\pm\frac{1,11}{1,5} =\pm\frac{1}{1,5} ,\pm\frac{11}{1,5}=\pm\frac{1}{1} ,\pm\frac{11}{1}\pm\frac{1}{5} ,\pm\frac{11}{5}\\\\\\\text{Hence the potential roots are }\\\\\pm1,\pm11,\pm\frac{1}{5},\pm\frac{11}{5}[/tex]
