Question

Решите по формулам Дискриминанта D= b²- 4ac ; x 1,2 = -b±√D ÷ 2a 1) 5x² - 8x - 4 = 0 2)4x² - 4x - 3 = 0 3)8x² - 6x + 1 = 0 4)5x² - 26x + 5 = 0

Answer 1

Ответ:

$1.5x {}^{2} - 8x - 4 = 0 \\ d = {b}^{2} - 4 ac = 64 - 4 \times 5 \times ( - 4) = 65 + 80 = 144 \\ \sqrt{d } = \sqrt{144} = 12 \\ x = \frac{b± \sqrt{d} }{2a} = \frac{8±12}{10} = 2 \: \: : - 0.4$

$2.4x {}^{2} - 4x - 3 = 0 \\ d = b{}^{2} - 4ac = 16 - 4 \times 4 \times ( - 3) = 16 + 48 = 64 \\ \sqrt{} d = \sqrt{64} = 8 \\ x = \frac{b± \sqrt{} d}{2a} = \frac{4±8}{8} = 1.5 \: \: : - 0.5$

$3.8x {}^{2} - 6x + 1 = 0 \\ d = b {}^{2} - 4ac = 36 - 4 \times 8 \times 1 = 4 \\ \sqrt{} d = \sqrt{4} = 2 \\ x = \frac{b± \sqrt{d} }{2a} = \frac{6±2}{16} = 0.25 \: \: 0.5:$

$4.d = b {}^{2} - 4ac = 676 - 4 \times 5 \times 5 = 576 \\ \sqrt{} d = \sqrt{576} = 24 \\ x = \frac{b± \sqrt{d} }{2a} = \frac{26±24}{10} = 0.2 \: \: : 5$

Answer 2

1) x1=-2/5; x2=2
2)x1=1/2; x2=3/2
3)x1=1/4; x2=1/2
4)x1=1/5; x2=5

Answer 3

Для решения квадратных уравнений по формулам дискриминанта и квадратного корня, мы должны найти значения дискриминанта (D) и затем использовать его, чтобы найти корни уравнения.

Уравнение квадратной формы: ax² + bx + c = 0

1. 5x² - 8x - 4 = 0 a = 5, b = -8, c = -4

D = b² - 4ac D = (-8)² - 4 * 5 * (-4) D = 64 + 80 D = 144

Теперь используем формулу для нахождения корней:

x1 = (-b + √D) / (2a) x1 = (8 + √144) / (2 * 5) x1 = (8 + 12) / 10 x1 = 20 / 10 x1 = 2

x2 = (-b - √D) / (2a) x2 = (8 - √144) / (2 * 5) x2 = (8 - 12) / 10 x2 = -4 / 10 x2 = -0.4

2. 4x² - 4x - 3 = 0 a = 4, b = -4, c = -3

D = (-4)² - 4 * 4 * (-3) D = 16 + 48 D = 64

x1 = (4 + √64) / (2 * 4) x1 = (4 + 8) / 8 x1 = 12 / 8 x1 = 1.5

x2 = (4 - √64) / (2 * 4) x2 = (4 - 8) / 8 x2 = -4 / 8 x2 = -0.5

3. 8x² - 6x + 1 = 0 a = 8, b = -6, c = 1

D = (-6)² - 4 * 8 * 1 D = 36 - 32 D = 4

x1 = (6 + √4) / (2 * 8) x1 = (6 + 2) / 16 x1 = 8 / 16 x1 = 0.5

x2 = (6 - √4) / (2 * 8) x2 = (6 - 2) / 16 x2 = 4 / 16 x2 = 0.25

4. 5x² - 26x + 5 = 0 a = 5, b = -26, c = 5

D = (-26)² - 4 * 5 * 5 D = 676 - 100 D = 576

x1 = (26 + √576) / (2 * 5) x1 = (26 + 24) / 10 x1 = 50 / 10 x1 = 5

x2 = (26 - √576) / (2 * 5) x2 = (26 - 24) / 10 x2 = 2 / 10 x2 = 0.2

Итак, корни уравнений:

1. x1 = 2, x2 = -0.4
2. x1 = 1.5, x2 = -0.5
3. x1 = 0.5, x2 = 0.25
4. x1 = 5, x2 = 0.2