Question

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

Answer 1

Given:

The function is

`f(x)=3x^3+2x^2+x+4`

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

`x=\frac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}`

We have,

`f(x)=3x^3+2x^2+x+4`

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

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

Clearly,
`(4)/(3),1,2` are possible roots but
`(3)/(4)` is not the possible root.

Therefore, the correct option is C.