Question

State all POSSIBLE rational zeros of the function f(x) = 3x^7 - 4x + 4.

Answer 1

Answer:

$\pm 1, \pm 2,\pm 4, \pm\dfrac{1}{3},\pm\dfrac{2}{3}, \pm\dfrac{4}{3}$

Step-by-step explanation:

The given function is

$f(x)=3x^7-4x+4$

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

$x=\frac{p}{q}$

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).

$\pm 1, \pm 2,\pm 4, \pm\dfrac{1}{3},\pm\dfrac{2}{3}, \pm\dfrac{4}{3}$.