The roots of $48{\mathrm{x}}^3 – 44{\mathrm{x}}^2 + 12\mathrm{x} – 1 = 0$ are in

$\begin{array}{l}Given48x^3-44x^2+12x-1=0\\ Leta=48,b=-44,c=12,d=-1\\ IfrootsareinA.P.thena{b}^3+27a^{2}d=9abc\\ 48{(-44)}^3+27{\left(48\right)}^2(-1)\ne 9\left(48\right)(-44)\left(12\right)\\ IfrootsareinG.Pthena{c}^3=b^{3}d\\ \Rightarrow 48{\left(12\right)}^3\ne {(-44)}^3(-1)\\ IftherootsareinH.Pthen\\ 2c^3+27a{d}^2=9bcd\\ \Rightarrow 2{\left(12\right)}^3+27\left(48\right){(-1)}^2=9(-44)\left(12\right)(-1)\\ \Rightarrow 4752=4752\\ \therefore rootsareinH.P\end{array}$