Question

помогите срочно на фото вопросы

Answer 1

6.

${x}^{2} + 15x + q = 0 \\ x_1 = - 12 \\ \\ (x + 12)(x - x2) = 0 \\ {x}^{2} + 12x - 12x_2 - xx_2 = 0 \\ {x}^{2} + (12 - x_2)x -12x_2 = 0 \\ \\ {x}^{2} + (12 - x_2)x - 12x_2 = {x}^{2} + 15x + q = 0$

Отсюда

$12 - x_2 = 15 \\ x_2 = - 3$

- второй корень

$q = - 12x_2 = - 12 \times ( - 3) = 36$

Ответ: - 3

7.

${x}^{2} + px - 32 = 0 \\ x_1 = 8 \\ \\ (x - 8)(x - x_2) = 0 \\ {x}^{2} - xx_2 - 8x + 8x_2 = 0 \\ {x}^{2} + ( - 8 - x_2)x + 8 x_2 = 0 \\ \\ {x}^{2} + ( - 8 - x_2)x + 8x_2 = {x}^{2} + px - 32 = 0 \\ \\ 8x_2 = - 32 \\ x_2 = - 4 \\ \\ p = - 8 - x_2 = - 8 + 4 = - 4$

Ответ: -4