Rozwiąż równanie, nierówności: a) [latex] x^{2} [/latex] - 2x +2 =0 b) 2[latex] x^{2} [/latex] + x -1[latex] geq [/latex]0 c) -[latex] x^{2} [/latex] + 11x -18 <0 d) -3 (x-2)(x+4)>0

[latex]a)x^2-2x+2=0\a=1, b=-2,c=2\ Delta=b^2-4ac=(-2)^2-4*1*(2)=4-8=-4\Delta<0; xepsilono \\b)2x^2+x-1 geq 0\a=2, b=1, c=-1\Delta=b^2-4ac=1-4*2*(-1)=1+8=9\sqrtDelta=3\x_1=frac{-b-sqrtDelta}{2a}=frac{-1-3}{4}=frac{-4}{4}=-1\x_2=frac{-b+sqrtDelta}{2a}=frac{-1+3}{4}=frac{2}{4}=frac{1}{2} \ a>0\2x^2+x-1ge0iff xepsilon(-infty,-1>cup0\ozn.:W(x)=-3(x-2)(x+4)\W(x)=0iff x-2=0 vee x+4=0\W(x)=0iff xepsilon{2,-4}\a_n<0\W(x)>0 iff xepsilon (-4,2)[/latex]