Number of transformed equations of
${\mathrm{x}}^4+2{\mathrm{x}}^3–12{\mathrm{x}}^2+2\mathrm{x}–1=0$ by eliminating third term is

$\begin{array}{l}Asweknowfortransformationy=x+h\\ hcanbeobtainedbydifferentiaction\\ \because Wehavetoremove{x}^2,sowehavedifferentiatctwice\\ \therefore f\left(x\right)=x^4+2x^3-12x^2+2x-1=0\\ f^{\text{'}}\left(x\right)=4x^3+6x^2-24x+12\\ f^{\text{'}\text{'}}\left(x\right)=12x^2+12x-24\\ \therefore f^{\text{'}\text{'}}\left(h\right)=0\Rightarrow 12h^2+12h-24=0\\ solvingthisweget2valuesfor\text{'}h\text{'}\end{array}$