The possible rational roots of the polynomial function are [tex]\pm 1[/tex], [tex]\pm 1/3[/tex], and [tex]\pm5[/tex] and this can be determined by using the given data.
Given :
[tex]\rm F(x) = 3x^2-3x+5[/tex]
The following steps can be used in order to determine the possible rational roots of the polynomial function:
Step 1 - Write the given polynomial equation.
[tex]\rm F(x) = 3x^2-3x+5[/tex]
Step 2 - The rational roots are the factors of the constant divided by the factors of the coefficient of [tex]\rm x^2[/tex].
Step 3 - So, the possible roots of the polynomial function are:
[tex]\dfrac{c}{a} = \dfrac{5}{3}=\pm \left(1,\dfrac{1}{3},5,\dfrac{5}{3}\right)[/tex]
Therefore, the correct options are A) [tex]\pm 1[/tex], B) [tex]\pm5[/tex], and C) [tex]\pm 1/3[/tex].
For more information, refer to the link given below:
https://brainly.com/question/13395232
