Answer:
[tex]\pm 1, \pm 2,\pm 4, \pm\dfrac{1}{3},\pm\dfrac{2}{3}, \pm\dfrac{4}{3}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=3x^7-4x+4[/tex]
We need to find all POSSIBLE rational zeros of the function f(x).
According to rational root theorem, all possible rational zeros of a polynomial are
[tex]x=\frac{p}{q}[/tex]
where, p is factors of constant and q is factors of leading term.
In the given function constant is 4 and leading term is 3.
Factors of 4 are ±1, ±2, ±4.
Factors of 3 are ±1, ±3.
All POSSIBLE rational zeros of the function f(x).
[tex]\pm 1, \pm 2,\pm 4, \pm\dfrac{1}{3},\pm\dfrac{2}{3}, \pm\dfrac{4}{3}[/tex].
