ANSWER
[tex]\pm1,\pm11,\pm \frac{1}{5} \pm \frac{11}{5} [/tex]
EXPLANATION
The given function is;
[tex]f(x) = 5 {x}^{2} - 7x + 11[/tex]
The constant term is 11.
The coefficient of the leading term is 5.
The factors of 11 are ±1,±11
The factors of 5 are ±1,±5
According to the Rational roots Theorem,
the potential roots are obtained by expressing the factors of the constant term over the coefficient of the leading term.
[tex]\pm1,\pm11,\pm \frac{1}{5} \pm \frac{11}{5} [/tex]
