What are the possible rational zeros of f(x) = 3x⁴ + x³ - 13x² - 2x + 9?

Solution:

It is given that

f(x) = 3x⁴ + x³ - 13x² - 2x + 9

The rational roots theorem states that any rational root will be a factor of the constant over a factor of the leading coefficient.

In the given equation, it is a factor of 9 over a factor of 3.

Here the factors of 9 are ±1, ±3, ±9 

Factors of 3 are ±1, ±3 

Therefore, the possible rational zeros are ±1, ±3, ±9, ±1/3.

What are the possible rational zeros of f(x) = 3x⁴ + x³ - 13x² - 2x + 9?

Summary:

The possible rational zeros of f(x) = 3x⁴ + x³ - 13x² - 2x + 9 are ±1, ±3, ±9, ±1/3.