Решите уравнение a) 12x^2+36x=0 б) 2x^2-7x-15=0

a) 12x^2+36x=0

12x (x+3) = 0

12x = 0

x = 0

и

x + 3 = 0

x = - 3

Ответ: 0; - 3

б)

2x^2 - 7x - 15 = 0

Штучный способ:

2x^2/2 - 7x - 15*2 = 0

x - > a

a^2 - 7a - 30 = 0

a1 = 10

a2 = - 3

x1 = 10/2 = 5;

x2 = - 3/2 = - 1,5

Ответ: 5; - 1,5;

Через дискриминант:

2x^2 - 7x - 15 = 0

a=2; b=-7; c=-15

D = b^2 - 4ac = (-7) ^2 - 4 * 2 * (-15) = 49 + 120 = 169 = 13^2

D>0

x1 = - b + √D/2a = 7 + 13/2*2 = 20/4 = 5;

x2 = - b - √D/2a = 7 - 13/2*2 = - 6/4 = - 3/2 = - 1,5;

Ответ: 5; - 1,5;