1)3ax^2-2(3a-2)x+3(a-1)=0 2)x(x-1)(x-2)(x-3)=15 3)x^4-x^3-10x^2+2x+4=0

Найдем корни.

1) 3 * a * x^2 2 * (3 * a - 2) * x + 3 * (a - 1) = 0;

D = (-2 * (3 * a 2))^2 4 * 3 * a * (3 * (a 1)) = 4 * (9 * a^2 12 * a + 4) 12 * a * (3 * a 3) = 36 * a^2 36 * a + 16 36 * a^2 36 * a = 16 = 4^2;

x1 = (2 * (3 * a 2) + 4)/(2 * 3 * a) = (6 * a 4 + 4)/(6 * a) = 6 * a/(6 * a) = 1;

x2 = (6 * a 4 4)/(6 * a) = (6 * a 8)/(6 * a) = 1 4/3 * a.

2) x * (x - 1) * (x - 2) * (x - 3) = 15; 

(x^2 3 * x) * (x^2 2 * x 1 * x + 2) = 15;

(x^2 3 * x) * (x^2 3 * x + 2) = 15;

Пусть x^2 3 * x = a, тогда:

a * (a + 2) = 15;

a^2 + 2 * a 15 = 0;

D = 4 4 * 1 * (-15) = 4 + 4 * 15 = 4 + 60 = 64 = 8^2;

x1 = (-2 + 8)/(2 * 1) = (-2 + 8)/2 = 6/2 = 3;

x2 = (-2 8)/(2 * 1) = -10/2 = -5;

Ответ: х = 3 и х = -5.

3) x^4 - x^3 10 * x^2 + 2 * x + 4 = 0;  

Разделяем на x^2.

x^4/x^2 - x^3/x^2 10 * x^2/x^2 + 2 * x/x^2 + 4/x^2 = 0; 

x^2 x 10 + 2/x + 4/x^2 = 0;

(x^2 + 4/x^2) (x 2/x) 10 = 0;

Пусть (x 2/x) = a.

(x 2/x)^2 = a^2;

x^2 2 * x * 2/x + 4/x^2 = a^2;

x^2 + 4/x^2 = a^2 + 4.  

Тогда: 

a^2 + 4 a 10 = 0;

a^2 a 6 = 0;

D = 1 4  * 1 * (-6) = 25;

a1 = (1 + 5)/2 = 3;

a2 = (1 5)/2 = -2;

Получаем:

1. x 2/x = 3;

x^2 3 * x 2 = 0;

D = 9 4 * 1 * (-2) = 17;

x1 = (3 + 17)/2;

x2 = (3 - 17)/2;

1. x 2/x = -2;

x^2 + 2 * x 2 = 0;

D = 4 4 * 1 * (-2) = 12;

x3 = (-2 + 12)/2 = -1 + 3;

x4 = (-2 - 12)/2 = -1 - 3.