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

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 1-ый 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 2-ой корень;

x3 = -2 3-ий 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 4-ый корень;

x5 = (-3 1)/2 = - 2 пятый корень.

Ответ.1; -1; - 2; 2; - 2.