6.
[tex]x^{6}-x^{5}-2x^{4} = 0\\\\x^{4}(x^{2}-x-2) = 0\\\\x^{4} = 0 \ \rightarrow \ x_{o} = 0\\\\lub\\\\x^{2}-x-2= 0\\\\\Delta = b^{2}-4ac = (-1)^{2}-4\cdot1\cdot(-2) = 1+8 = 9\\\\\sqrt{\Delta} = \sqrt{9} = 3\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-(-1)-3}{2\cdot1} = \frac{-2}{2} = -1\\\\x_2 = \frac{-(-b)+\sqrt{\Delta}}{2a} = \frac{-(-1)+3}{2} = \frac{4}{2} = 2\\\\x \in\{-1, 0, 2\}[/tex]
5.
[tex]L(x) = x^{3}-6x^{2}-2x+12 = x^{2}(x-6)-2(x-6) = (x-6)(x^{2}-2) =\\\\= (x-6)(x+\sqrt{2})(x-\sqrt{2})[/tex]
