Question

Решите квадратное уравнение

X² - 5x - 24 = 0

3X² - 4x - 5 = 0

Answer 1

х² - 5x - 24 = 0,

Д = (-5)² - 4*1*(-24) = 25 + 96 = 121,

х1 = (5 + 11) / 2*1 = 16/2 = 8,

х2 = (5 - 11) / 2*1 = -6/2 = -3,

3х² - 4х - 5 = 0,

Д = (-4)² - 4*3*(-5) = 16 + 60 = 76,

х1 = (4 + √76) / 2*3 = (4 + 2√19) / 2*3 = (2 + √19)/3,

х2 = (4 - √76) / 2*3 = (4 - 2√19) / 2*3 = (2 - √19)/3

Answer 2

1)
${x}^{2} - 5x - 24 = 0 \\ x_1= - 3 \\ x_2=8$
По теореме Виета

2)
$3 {x}^{2} - 4x - 5 = 0 \\ D=b^2-4ac \\ D= { - 4}^{2} - 4 \times 3 \times ( - 5) = 16 + 60 = 76 \\ x_1 = \frac{ - b + \sqrt{D} }{2a}; \: \: x_1 = \frac{4 + \sqrt{76} }{6} = \frac{4 + 2\sqrt{19} }{6} \\ x_2 = \frac{ - b - \sqrt{D} }{2a} ; \: \: x_2 = \frac{4 - 2 \sqrt{19} }{6}$
Через Дискриминант