Solution:
Given the function below
[tex]f\mleft(x\mright)=3x^6+4x^3-2x^2+4[/tex]For teh possible roots;
[tex]\begin{gathered} a_0=4,\:a_n=3 \\ \mathrm{The\:dividers\:of\:}a_0:1,\:2,\:4 \\ \begin{equation*} \mathrm{The\:dividers\:of\:}a_n:1,\:3 \end{equation*} \\ \mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\pm\frac{1,\:2,\:4}{1,\:3} \end{gathered}[/tex]From the deduction above,
The possible rational roots is
[tex]±1,\pm\frac{1}{3}\pm2,\pm\frac{2}{3},\pm4,\pm\frac{4}{3}.[/tex]Hence, all the possible zeros is
[tex][/tex]