Rational root theorem is used to determine the possible roots of a function.
The potential roots are: -3 and 3/2
The function is given as:
[tex]\mathbf{f(x) = 6x^3 - 2x^2 + x+3}[/tex]
For a function,
[tex]\mathbf{f(x) = px^n +.........+q}[/tex]
The potential roots are:
[tex]\mathbf{Root = \pm\frac{Factors\ of\ q}{Factors\ of\ p}}[/tex]
So, we have:
[tex]\mathbf{q = \pm 1, \pm 3}[/tex] ---- factors of 3
[tex]\mathbf{p = \pm 1, \pm 2, \pm 3, \pm 6}[/tex] ---- factors of 6
The potential roots are:
[tex]\mathbf{Root = \frac{\pm 1, \pm 3}{\pm 1, \pm 2, \pm 3, \pm 6}}[/tex]
From the options, the potential roots are:
[tex]\mathbf{Root = -3, \frac{3}{2}}[/tex]
Read more about rational roots theorem at:
https://brainly.com/question/9353378
