Question

решить через дискриминат

Answer 1

1.) x^2 - 3x + 4 = 0
D = b^2 - 4ac = (-3)^2 - 4 x 1 x (-4) = 9 + 16 = 25 = 5^2 , 2 корня.

x1 = -b - √D / 2a = 3 - 5 / 2 = -1
x2 = -b + √D / 2a = 3 + 5 / 2 = 4

Answer 2

2) 3х^2 - 1 > х
3х^2 - 1 - х = 0
Д = 1 - 4 • 3 • ( - 1) = 1 + 12 = 13 > 0.
х1 = 1 + √13 /6
х2 = 1 - √ 13 / 6.

3) 3х^2 < х^2 - 5х + 6
3х^2 - х^2 + 5х - 6
2х^2 + 5х - 6
Д = 25 - 4 • 2 • ( -6 ) = 25 + 48 = 73.
х1 = - 5 + √ 73 / 4
х2 = - 5 - √ 73 / 4.

4) 2х ( х + 1 ) < х + 5
2х^2 + 2х < х + 5
2х^2 + 2х - х - 5
2х^2 + х - 5 = 0
Д = 1 - 4 • 2 • ( -5 ) = 1 + 40 = 41.
х1 = - 1 + √41 / 4
х2 = -1 - √41 / 4.
Удачи)))