ZADANIE 1 [latex]W(x) = 2x + 1[/latex] [latex]P(x) = x^2 + 2x - 1[/latex] [latex]2 * W(x) - P(x) = 2 * (2x + 1) - (x^2 + 2x - 1) = 4x + 2 - x^2 - 2x + 1 =[/latex] [latex]= -x^2 + 2x + 3[/latex] ZADANIE 2 a) [latex]x^3 + 5x^2 - 6x = 0[/latex] [latex]x(x^2 + 5x - 6) = 0[/latex] [latex]x = 0 lub x^2 + 5x - 6 = 0[/latex] Zajmijmy się równaniem [latex]x^2 + 5x - 6 = 0[/latex] [latex]DELTA = 5^2 - 4 * (-6) = 25 - (-24) = 25 + 24 = 49[/latex] [latex]sqrt{DELTA} = sqrt{49} = 7[/latex] [latex]x_{1} = frac{-5 - 7}{2} = frac{-12}{2} = -6[/latex] [latex]x_{2} = frac{-5 + 7}{2} = frac{2}{2} = 1[/latex], zatem: [latex]x = 0 lub x = 1 lub x = (-6)[/latex] b) [latex]x^3 + 5x^2 - x - 5 = 0[/latex] [latex]x(x^2 - 1) + 5(x^2 - 1) = 0[/latex] [latex](x + 5)(x^2 - 1) = 0[/latex] [latex](x + 5)(x - 1)(x + 1) = 0[/latex] [latex]x + 5 = 0 lub x - 1 = 0 lub x + 1 = 0[/latex] [latex]x = (-5) lub x = 1 lub x = (-1)[/latex]
