Question

When using the rational root theorem, which of the following is a possible root of the polynomial function below? F(x) = 3x - x2 + 4x +5 ОА. б O B. -7 Ос O C. - D.

Answer 1

Given:

`f(x)3x^3-x^2+4x+5`

Since all coefficients are integers, we can apply the rational zeros theorem

The coefficient of the constant term is 5

The factors of 5 are +1, -1, +5, -5

These are the possible values for p

`p=\pm1,\pm5`

The leading coefficient (the coefficient of the term with the highest degree) is 3

The factors of 3 are +1, -1, +3, -3

These are the possible values for q

`q=\pm1,\pm3`

The possible rational roots are

`(p)/(q)=\pm1\pm(1)/(3),\pm5,\pm(5)/(3)_{}`

From the options provided the possible rational root is

-5/3, OPTION C