[tex]w(x)=4x^6-12x^5+x^4\\\\w(x)=x^4(4x^2-12x+1)\\\\{\qquad}\Delta=(-12)^2-4\cdot4\cdot1=144-16=128\quad\implies\quad\sqrt\Delta=8\sqrt2\\\\{\qquad}x_1=\frac{12-8\sqrt2}{2\cdot4}=\frac{3-2\sqrt2}2\ ,\qquad x_2=\frac{12+8\sqrt2}{2\cdot4}=\frac{3+2\sqrt2}2\\\\w(x)=4x^4(x-\frac{3-2\sqrt2}2)(x-\frac{3+2\sqrt2}2)[/tex]
