Using the rational root theorem, list out all possible/candidate rational roots for
f(x) = 4x^3 + 27x^2 - 13x + 17
Express your answer as integers or as fractions
The rational root theorem states that if a rational number p/q is a root of a polynomial with integer coefficients, then p must divide the constant term and q must divide the leading coefficient.
In this case, the constant term is 17 and the leading coefficient is 4.
The possible candidates for rational roots are therefore:
p (divides 17): ±1, ±17
q (divides 4): ±1, ±2, ±4
Combining all possible pairs from p and q, the list of possible/candidate rational roots for f(x) = 4x^3 + 27x^2 - 13x + 17 is:
±1/1, ±17/1, ±1/2, ±17/2, ±1/4, ±17/4.