According to the rational root theorem, which function had the same set of potential rational roots as the function g(x)= 3x^5 -2x^4 + 9x^3 -x^2 +12

  4,-4  ,2,-2 ,1 and -1 are the possible roots.

Step by step Solution

Here leading coefficient is 3 and constant term is 12

therefore number of rational roots are given by  ±.

therefore number of roots are  ± 4  which is divides by

+4 ,-4 ,+2 ,-2 ,+1 ,-1  ,using rational roots theorem

these are the possible roots of the given function

In order to find the actual roots we can check them using synthetic division method