Zad 1 a) (x - 2)(x + 3)(4x - 24) = 0 4(x - 2)(x + 3)(x - 6) = 0 x = 2 lub x = -3 lub x = 6 b) x³ + 2x² - 25x - 50 = 0 x²(x + 2) - 25(x + 2) = 0 (x² - 25)(x + 2) = 0 (x - 5)(x + 5)(x + 2) = 0 x = 5 lub x = -5 lub x = -2 c) x³ + 4x²- 27x - 90 = 0 x³ + 3x² + x² + 3x - 30x - 90 = 0 x²(x + 3) + x(x + 3) - 30(x + 3) = 0 (x² + x - 30)(x + 3) = 0 (x² - 5x + 6x - 30)(x + 3) = 0 [x(x - 5) + 6(x - 5)] (x + 3) = 0 (x + 6)(x - 5)(x + 3) = 0 x = -6 lub x = 5 lub x = -3 d) (x + 4)²(9x - 18)² x(x -10) = 0 x + 4 = 0 lub 9x - 18 = 0 lub x = 0 lub x - 10 = 0 x = -4 lub 9x = 18 lub x = 0 lub x = 10 x = -4 lub x = 2 lub x = 0 lub x = 10 e) 3x³ - 15x² - 4x + 20 = 0 3x²(x - 5) - 4(x - 5) = 0 (3x² - 4)(x - 5) = 0 3(x² - 4/3)(x - 5) = 0 3[x - (2√3)/3 ] [x + (2√3)/3 ] (x - 5) = 0 x = (2√3) / 3 lub x = -(2√3) / 3 lub x = 5
