The roots of $48x^3-44x^2+12x-1=0$  are in

$48-44x+12x^2-x^3=0$

$x^3-12x^2+44x-48=0$

$3a=12\Rightarrow a=4$

Roots are in A.P for $x^3-12x^2+44x-48=0$

$\therefore$ We can say that the roots are in H.P.