Which of the following is NOT a possible root of the function? (Hint: Use the rational root theorem, write out all the possible roots, and see which one is NOT on your list.) Please use any sources to help you. f(x)= 3x^3+2x^2+x+4

A. +4/3
B. +1
C. +3/4
D. +2

Given:

The function is

To find:

The value from the given options that is NOT a possible root of the function.

Solution:

According to rational root theorem, all possible roots are in the form of

We have,

Here,

Leading coefficient = 3.

Constant term = 4

Factors of 3 are ±1, ±3.

Factors of 4 are ±1, ±2, ±4.

Using rational root theorem, all possible roots of given functions are

Clearly, are possible roots but is not the possible root.

Therefore, the correct option is C.

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