Finding roots of cubic equation 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.
My attempt:
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?

Let $$f(x)=2x^3-3x^2-12x+1$$  
Now, 
$f(0)>0$ and $f(1)<0 \implies 0< \alpha <1$  
$f(-2)<0$ and $f(-1)>0 \implies -2< \beta <-1$  
$f(3)<0$ and $f(4)>0 \implies 3< \gamma <4$   
$\therefore \lfloor\alpha\rfloor + \lfloor\beta\rfloor + \lfloor\gamma\rfloor = 0+(-2)+3=1$
