Question

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

Answer 1

`\pm 1, \pm 2,\pm 4, \pm(1)/(3),\pm(2)/(3), \pm(4)/(3)`

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=(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(1)/(3),\pm(2)/(3), \pm(4)/(3)`.