Question

According to the rational root theorem, what are all the potential rational roots of f(x)= 5x^3-7x+11

Answer 1

The rational root theorem states that the rational roots of a polynomial can only be in the form p/q, where p divides the constant term, and q divides the leading term.

In your case, both the leading term 5 and the constant term 11 are primes, so their only divisors are 1 and themselves.

So, the only feasible solutions are

$\pm\dfrac{11}{5},\quad\pm 11,\quad \pm\dfrac{1}{5}, \pm 1$

For the record, in this case, none of the feasible solutions are actually a root of the polynomial.