Question

When using the rational root theorem, which of the following is a possible root of the polynomial function below f(x)=x^3-5x^2-12x+14

A.9
B.3
C.7
D.5

Answer 1

the answer is C.) 7

Answer 2

`\Large \boxed{\sf \ \ 7 \ \ }`

Explanation:

Hello, please consider the following.

The polynomial function is

`x^3-5x^2-12x+14`

The rational root theorem states that each rational solution

`x=(p)/(q)`

, written in irreducible fraction, satisfies the two following:

p is a factor of the constant term

q is a factor of the leading coefficient

In this example, the constant term is 14 and the leading coefficient is 1. It means that p is a factor of 14 and q a factor of 1.

Let's proceed with the prime factorisation of 14:

14 = 2 * 7

Finally, the possible rational roots of this expression are :

1

2

7

14

and we need to test for negative ones too

-1

-2

-7

-14

From your list, the correct answer is 7.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you