[latex]W(x)=-2x^{3}+kx^{2}+4x-8\\W(-1)=-6\\-6=-2cdot(-1)^{3}+kcdot(-1)^{2}+4cdot(-1)-8\\-6=2+k-4-8\\-6=k-10\\k=4[/latex] [latex]W(x)=-2x^{3}+4x^{2}+4x-8\\W(x)+8=0\\-2x^{3}+4x^{2}+4x-8+8=0\\-2x^{3}+4x^{2}+4x=0\\x^{3}-2x^{2}-2x=0\\x(x^{2}-2x-2)=0\\Delta=(-2)^{2}-4cdot1cdot(-2)=4+8=12\\sqrt{Delta}=2sqrt{3}[/latex] [latex]x_{1}=frac{2sqrt{3}+2}{2}=sqrt{3}+1\\x_{2}=frac{-2sqrt{3}+2}{2}=-sqrt{3}+1\\xin{-sqrt{3}+1;0;sqrt{3}+1}[/latex]
W(-1)=2+k-4-8=-6 k-10=-6 k=-6+10 k=4 [latex]\-2x^3+4x^2+4x-8 +8=0 \ \x=0 vee x^2-2x-2=0 \ \-2x(x^2-2x-2)=0 \ \Delta=2^2+4*2=4+8=12 \ \sqrtDelta=2sqrt3 \ \x_1=frac12(2-2sqrt3)=1-sqrt3, x_2=1+sqrt3 \ \Odp. xin{1-sqrt3, 0, 1+sqrt3}[/latex]
