Answer:
[tex]\pm11,\pm1,\pm\frac{11}{5},\pm\frac{1}{5}[/tex]
Step-by-step explanation:
The given polynomial function is
[tex]f(x)=5x^3-7x+11[/tex]
According to the Rational Roots Theorem, the ratio of all factors of the constant term expressed over the factors of the leading coefficient.
The potential rational roots are
[tex]\pm\frac{11}{1}=\pm11[/tex]
[tex]\pm\frac{1}{1}=\pm1[/tex]
[tex]\pm\frac{11}{5}[/tex]
[tex]\pm\frac{1}{5}[/tex]
