W(x)=-2x3+kx2 +4x-8 W(-1)=-6 W(-1)=(-2)(-1)³+k*(-1)²+4(-1)-8=-2+k-4-8=k-14 k-14=-6 k=14-6=8 W(x)+8=0 -2x³+8x²+4x-8+8=0 -2x³+8x²+4x=0 (-2x)(x²-4x-2)=0 -2x=0 x=0 lub x²-4x-2=0 Δ=(-4)²-4*1*(-2)=16+8=24 √Δ=2√6 x1=(4-2√6)/2=2-√6 x2=(4+2√6)/2=2+√6 odp. k=8 x∈{2-√6, 0, 2+√6}
Skoro [latex]W(-1)=-6 \[/latex] to [latex] -2(-1)^3 + k(-1)^2 + 4(-1) -8 = -6[/latex] => [latex]2+k-4 - 8 = -6 \ k=4 \ W(x) +8 = 0 \ -2x^3 + 4x^2 + 4x = 0 \ 2x(-x^2 + 2x + 2)=0\ x_0=0\ \ 2^2 -4(-1*2) = 4 + 8 = 12[/latex] [latex]x_{1} =frac{-2 - sqrt{12}}{2}[/latex], [latex]x_{2} =frac{-2 + sqrt{12}}{2}[/latex], [latex]x_0=0[/latex]
