Question

According to the rational root theorem which of the following are possible roots of the polynomial function below? Check all that apply

f(x)=6x^3-7x^2+2x+8


(answer choices in pic)

Answer 1

Apex

-1/6

2/3

-8

4

xoxo

Answer 2

By using the rational root theorem the possible choices are A, B, C and E

Explanation:

The rational root theorem states that if the leading coefficient is taken to be an and the constant coefficient is taken to be a0 the possible roots of the equation can be expressed as :

`\pm\frac{\text{factors of }a_0}{\text{Factors of }a_n}\\\\=\pm(1,2,4,8)/(1,2,3,6)`

Now, from the given options, the possible choices can be :

A, B, C and E

D can be there because after taking any pair the rational root can't be 3

F can't be possible because an does't have 4 in its factors so denominator cannot be 4.

Hence, by using the rational root theorem the possible choices are A, B, C and E