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

Step-by-step explanation:

Hello, please consider the following.

The polynomial function is

The rational root theorem states that each rational solution

, 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

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step-by-step explanation:

sorry no step by step

the square root of what number? if you add that, then someone will probably answer the question.