1a) 2[latex]x^{4}[/latex] - 8[latex] x^{3}[/latex] + 6 [latex]x^{2}[/latex] = 0 2[latex] x^{2} [/latex] ([latex] x^{2}[/latex] - 4x +3) = 0 [latex] 2x^{2}[/latex] = 0 [latex] x^{2}[/latex] -4x+3=0 x=0 delta = 16 -12 =4 sqrt{delty}=2 [latex] x_{1}[/latex] = [latex] frac{4-2}{2} [/latex]=1 [latex] x_{2}[/latex] = [latex] frac{4+2}{2} [/latex]= 3 b) 4[latex] x^{3} [/latex] - 4[latex] x^{2} [/latex] - 9x+9=0 4[latex] x^{2} [/latex] (x-1) -9(x-1)=0 (4[latex] x^{2} [/latex]-9)= 0 x-1=0 4[latex] x^{2} [/latex]=9 x=1 [latex] x^{2} [/latex]=[latex] frac{9}{4} [/latex] x=[latex] sqrt{ frac{9}{4} } [/latex] lub x=-[latex] sqrt{ frac{9}{4} } [/latex] --> x=[latex] frac{3}{2} [/latex] lub x= - [latex] frac{3}{2} [/latex] 2a) 4[latex] x^{2} [/latex]= -12x-9 4[latex] x^{2} [/latex]+12x+9=0 delta= 144-144=0 [latex] x_{0} [/latex]=[latex] frac{-12}{8} [/latex] = -1[latex] frac{1}{2} [/latex] b) x^2+x-2≥0 [latex] x^{2} [/latex]+x-2[latex] geq [/latex]0 delta= 1+8= 9 [latex] sqrt{delty} [/latex]=3 [latex] x_{1} [/latex]= [latex] frac{-1-3}{2} =-2[/latex] [latex] x_{2} = frac{-1+3}{2} = 1[/latex]
