Question

Nierówności kwadratowe:

1) -2x² + 9 - 9 < 0

2) -3x² + 7x - 2 ≥ 0

3) 15 - 2x - x² ≤ 0

Answer 1

1)

-2x² + 9 - 9 < 0

-2x² < 0 |:(-2)

x² < 0

x < 0

 

2)

-3x² + 7x - 2 ≥ 0

a=-3  b=7  c=-2

Δ = b²-4ac

Δ = 7² - 4*(-3)*(-2)

Δ = 49-24

Δ = 25

x₁ = (-b-√Δ)/2a

x₁ = (-7-5)/-6 = -12/-6 = 2

x₂ = (-b+√Δ)/2a

x₂ = (-7+5)/-6 = -2/-6 = 1/3

x∈<1/3, 2>

 

3)

15 - 2x - x² ≤ 0

a=-1 b=-2 c=15

Δ = b²-4ac

Δ = (-2)²-4*(-1)*15

Δ = 4+60

Δ = 64

√Δ = 8

x₁ = (-b-√Δ)/2a

x₁ = (2-8)/-2 = -6/-2 = 3

x₂ = (-b+√Δ)/2a

x₂ = (2+8)/-2 = 10/-2 = -5

x∈<-∞,-5> u <3,+∞>