Question

Запишите многочлен третьей степени, корни которого равны: 1) -1; 0; 2; 2) -2; 2; 1; 3) -2; 1; 3; 4) -2; -1; 4.​

Answer 1

Ответ:

${x}^{3} - {x}^{2} - 2x = x(x + 1)(x - 2) = 0 \\ {x}^{3} - {x}^{2} - 4x + 4 = (x + 2)(x - 2)(x - 1) = ( {x}^{2} - 4)(x - 1) = 0 \\ {x}^{3} - 2 {x}^{2} - 5x + 6 = (x + 2)(x - 1)(x - 3) = 0 \\ {x}^{6} - {x}^{2} - 10x - 8 = (x + 2)(x + 1)(x - 4) = 0$