Решите уравнение: x5 + 2x4 - 3x3 - 6x2 + 2x + 4 = 0

x^5 + 2x^4 - 3x^3 - 6x^2 + 2x + 4 = 0;(x^5 + 2x^4 - 3x^3) + (- 6x^2 + 2x + 4) = 0;x^3(x^2 + 2x – 3) – 2(3x^2 – x – 2) = 0.Разложим на множители выражения (x^2 + 2x – 3) и (3x^2 – x – 2).x^2 + 2x – 3 = 0;D = b^2 – 4ac;D = 4 + 4 * 3 = 4 + 12 = 16; √D = 4;x = (-b ± √D)/(2a);x1 = (-2 + 4)/2 = 1;x2 = (-2 – 4)/2 = - 3;x^2 + 2x – 3 = (x – 1)(x + 3).3x^2 – x – 2 = 0;D = b^2 – 4ac;D = 1 + 4 * 3 * 2 = 25; √D = 5;x = (-b ± √D)/(2a);x1 = (1 + 5)/6 = 1;x2 = (1 – 5)/6 = -4/6 = -2/3;3x^2 – x – 2 = 3(x + 2/3)(x – 1) = (3x + 2)(x – 1).x^3(x – 1)(x + 3) - 2(3x + 2)(x – 1) = 0;(x – 1)(x^3(x + 3) – 2(3x + 2)) = 0;x – 1 = 0;x1 = 1 – первый корень;x^3(x + 3) – 2(3x + 2) = 0;x^4 + 3x^3 – 6x – 4 = 0;(x^4 – 4) + (3x^3 – 6x) = 0;(x^2 – 2)(x^2 + 2) + 3x(x^2 – 2) = 0;(x^2 – 2)(x^2 + 2 + 3x) = 0;x^2 – 2 = 0;x^2 = 2;x2 = √2 – второй корень;x3 = -√2 – третий корень;x^2 + 2 + 3x = 0;D = b^2 – 4ac;D = 9 – 4 * 2 = 1; √D = 1;x = (-b ± √D)/(2a);x4 = (-3 + 1)/2 = -1 – четвертый корень;x5 = (-3 – 1)/2 = - 2 –пятый корень.Ответ.1; -1; - 2; √2; - √2.