1. [latex]W(x) = x^5 + 5x^4 +3x^3 +15x^2 \\ x^5 + 5x^4 +3x^3 +15x^2 = 0 \ x^4 cdot (x + 5)+3x^2 cdot (x +5) = 0 \ (x + 5)(x^4 + 3x^2) = 0 \ (x + 5) cdot x^2 cdot (x^2 + 3) = 0 \ x^2(x + 5)(x^2 + 3) = 0 \ x^2 = 0 lub x + 5 lub x^2 + 3 = 0 \\ x^2 = 0 \ x = 0 \\ x +5 = 0 \ x = - 5 \\ x^2 + 3 = 0 \ x^2 = - 3 \ sprzeczno's'c - r'ownanie nie ma rozwiaza'n[/latex] Odp. x = - 5 i x = 0 [latex]W(x) = x^4 - 9x^3 + 2x^2 - 18x \\ x^4 - 9x^3 + 2x^2 - 18x = 0 \ x^3 cdot (x - 9) + 2x cdot (x - 9) = 0 \ (x - 9)(x^3 + 2x) = 0 \ (x - 9) cdot x cdot (x^2 + 2) = 0 \ x(x - 9)(x^2 + 2) = 0 \ x = 0 lub x - 9 = 0 lub x^2 + 2 = 0 \\ x = 0 \\ x - 9 = 0 \ x = 9 \\ x^2 + 2 = 0 \ x^2 = - 2\ sprzeczno's'c - r'ownanie nie ma rozwiaza'n[/latex] Odp. x = 0 i x = 9 2. [latex]8(y+1) + (y+1)^2- 3 - 5(-7y + 5)^2+ 4y = 8y + 8 + y^2 +2y + \ + 1 - 3 - 5(49y^2 - 70y + 25) + 4y = 8y + 8 + y^2 +2y + 1 - 3 -\ 245y^2 + 350y - 125 + 4y = -244y^2 + 364y - 119[/latex] 3. [latex]W(x) = (x-3)^2 cdot (2x-9) \\ (x-3)^2 cdot (2x-9) = 0 \ (x-3)^2 = 0 lub 2x-9 = 0 \\ (x-3)^2 = 0 \ x - 3 = 0 \ x = 3 \ pierwiastek 2-krotny \\ 2x-9 = 0 \ 2x = 9 /:2 \ x = 4,5 \ pierwiastek 1-krotny [/latex] Odp. x = 3 pierwiastek 2-krotny, x = 4,5 pierwiastek 1-krotny
