Question

прорешайте по курсу 9 кл)

Answer 1

Ответ:

Объяснение:

Решение дано на фото.

Answer 2

a) ${x}^{2} - 2x - 15 = 0$

$D = {b}^{2} - 4ac = {( - 2)}^{2} - 4 \times 1 \times ( - 15) = 4 + 60 = 64 = {8}^{2}$

$x_1 = \frac{ - b + \sqrt{D} }{2a} = \frac{ 2 + 8}{2 \times 1} = \frac{10}{2} = 5$

$x_2 = \frac{ - b - \sqrt{D} }{2a} = \frac{2 - 8}{2 \times 1} = \frac{ - 6}{2} = - 3$

Ответ: -3; 5

б) ${x}^{2} + 2x - 8 = 0$

$D = {b}^{2} - 4ac = {2}^{2} - 4 \times 1 \times ( - 8) = 4 + 32 = 36 = {6}^{2}$

$x_1 = \frac{ - b + \sqrt{D} }{2a} = \frac{ - 2 + 6}{2 \times 1} = \frac{4}{2} = 2$

$x_2 = \frac{ - b - \sqrt{D} }{2a} = \frac{ - 2 - 6}{2 \times 1} = \frac{ - 8}{2} = - 4$

Ответ: -4; 2

в) ${x}^{2} + 10x + 9 = 0$

$D = {b}^{2} - 4ac = {10}^{2} - 4 \times 1 \times 9 = 100 - 36 = 64 = {8}^{2}$

$x_1 = \frac{ - b + \sqrt{D} }{2a} = \frac{ - 10 + 8}{2 \times 1} = \frac{ - 2}{2} = - 1$

$x_2 = \frac{ - b - \sqrt{D} }{2a} = \frac{ - 10 - 8}{2 \times 1} = \frac{ - 18}{2} = - 9$

Ответ: -9; -1

г) ${x}^{2} - 12x + 35 = 0$

$D = {b}^{2} - 4ac = {( - 12)}^{2} - 4 \times 1 \times 35 = 144 - 140 = 4 = {2}^{2}$

$x_1 = \frac{ - b + \sqrt{D} }{2a} = \frac{12 + 2}{2 \times 1} = \frac{14}{2} = 7$

$x_2 = \frac{ - b - \sqrt{D} }{2a} = \frac{12 - 2}{2 \times 1} = \frac{10}{2} = 5$

Ответ: 5; 7

д) $3 {x}^{2} + 14x + 16 = 0$

$D = {b}^{2} - 4ac = {14}^{2} - 4 \times 3 \times 16 = 196 - 192 = 4 = {2}^{2}$

$x_1 = \frac{ - b + \sqrt{D} }{2a} = \frac{ - 14 + 2}{2 \times 3} = \frac{ - 12}{6} = - 2$

$x_2 = \frac{ - b - \sqrt{D} }{2a} = \frac{ - 14 - 2}{2 \times 3} = \frac{ - 16}{6} = - \frac{8}{3}$

Ответ: - 8/3; -2

е) $2 {x}^{2} - 5x + 6 = 0$

$D = {b}^{2} - 4ac = {( - 5)}^{2} - 4 \times 2 \times 6 = 25 - 48 = - 23$

D < 0, корней уравнения нет

Ответ: корней нет

ж) ${x}^{2} - 2x + 1 = 0$

$D = {b}^{2} - 4ac = {( - 2)}^{2} - 4 \times 1 \times 1 = 4 - 4 = 0$

D = 0, корень уравнения один

$x = \frac{ - b}{2a} = \frac{2}{2 \times 1} = \frac{2}{2} = 1$

Ответ: 1

з) ${x}^{2} + 4x + 4 = 0$

$D = {b}^{2} - 4ac = {4}^{2} - 4 \times 1 \times 4 = 16 - 16 = 0$

D = 0, корень уравнения один

$x = \frac{ - b}{2a} = \frac{ -4 }{2 \times 1} = - \frac{4}{2} = - 2$

Ответ: -2

и) ${x}^{2} - 6x + 9 = 0$

$D = {b}^{2} - 4ac = {( - 6)}^{2} - 4 \times 1 \times 9 = 36 - 36 = 0$

D = 0, корень уравнения один

$x = \frac{ - b}{2a} = \frac{6}{2 \times1 } = \frac{6}{2} = 3$

Ответ: 3

к) $4 {x}^{2} + 7x - 2 = 0$

$D = {b}^{2} - 4ac = {7}^{2} - 4 \times 4 \times ( - 2) = 49 + 32 = 81 = {9}^{2}$

$x_1 = \frac{ - b + \sqrt{D} }{2a} = \frac{ - 7 + 9}{2 \times 4} = \frac{2}{8} = \frac{1}{4}$

$x_2 = \frac{ - b - \sqrt{D} }{2a} = \frac{ - 7 - 9}{2 \times 4} = \frac{ - 16}{8} = - 2$

Ответ: -2; 1/4

л) $5 {x}^{2} - 9x - 2 = 0$

$D = {b}^{2} - 4ac = {( - 9)}^{2} - 4 \times 5 \times ( - 2) = 81 + 40 = 121 = {11}^{2}$

$x_1 = \frac{ - b + \sqrt{D} }{2a} = \frac{9 + 11}{2 \times 5} = \frac{20}{10} = 2$

$x_2 = \frac{ - b - \sqrt{D} }{2a} = \frac{ 9 - 11}{2 \times 5} = \frac{ - 2}{10} = - 0.2$

Ответ: -0.2; 2

м) $2 {x}^{2} - 11x + 15 = 0$

$D = {b}^{2} - 4ac = {( - 11)}^{2} - 4 \times 2 \times 15 = 121 - 120 = 1 = {1}^{2}$

$x_1 = \frac{ - b + \sqrt{D} }{2a} = \frac{11 + 1}{2 \times 2} = \frac{12}{4} = 3$

$x_2 = \frac{ - b - \sqrt{D} }{2a} = \frac{11 - 1}{2 \times 2} = \frac{10}{4} = \frac{5}{2} = 2.5$

Ответ: 2.5; 3