If $\alpha,\beta,\gamma $ are the roots of the equation $2x^3-3x^2-12x+1=0$.Then find the value of [$\alpha$]+[$\beta$]+[$\gamma$],where [.] denotes greatest integer function.
I first tried hit and trial to guess the first root but no luck.Then I tried rational root method, but its roots are not rational (both roots could not satisfy the equation.)
I think its roots are irrational. Can someone help me finding its roots?