Question

Rozwiąż równania:

a) 3x²+ 4x – 4 = 0
b)–x² – 3x + 4= 0

c)-x² + 3x – 2 = 0

d) 3x²+ 2x – 1 = 0

e) x ( x – 9 ) = 10

f) – x²+ 5x = 0

g)3x² + 12x = 0

h)x² – 4 = 0

Answer 1

a)

Δ=16+48=64

x=(-4-8)/6= -2 lub x=(-4+8)/6=2/3

b)

Δ=9+16=25

x=(3-5):(-2)= 1 lub x= -4

c)

Δ=9-8=1

x=(-3-1):(-2)=2 lub x= 1

d)

Δ=4+12=16

x=(-2-4)/6= -1 lub x=2/6=1/3

e)

x=0 lub x-9=0

Odp. x=0 v x=9

f)

-x(x-5)=0

x=0 v x=5

g)

3x(x+4)=0

x=0 v x=-4

h)

(x+2)(x-2)=0

x=-2 v x=2

Answer 2

a) 3x²+ 4x – 4 = 0 

 Δ = b² - 4ac

Δ = 16 + 48 =64

√Δ = 8

x₁ = -b-√Δ/2a

x₁ = -4-8/6

x₁ = -2

x₂= -b+√Δ/21

x₂ = -4+8/6

x₂ = ⅔

Odp. x₁ = -2 x₂ = ⅔
b)–x² – 3x + 4= 0

Δ = 9 + 16 = 25

√Δ =5

x₁ = 3-5/-2

x₁ = 1

x₂ = 3+5/-2

x₂ = -4

Odp. x₁ = 1 x₂ = -4

c)-x² + 3x – 2 = 0

Δ = 9 - 8 =1

√Δ =1

x₁ = -3-1/-2

x₁ = 2

x₂ = x₁ = -3+1/-2

x₂ = 1

Odp. x₁ = -1 x₂ = -2

d) 3x²+ 2x – 1 = 0

Δ = 4 + 12 =16

√Δ =4

x₁ = -2-4/6

x₁ = -1

x₂ = -2+4/6

x₂ = ⅓

Odp. x₁ = -1  x₂ = ⅓

e) x ( x – 9 ) = 10

x² - 9x - 10 = 0

Δ = 81 + 40 = 121

√Δ = 11

x₁ = 9-11/2

x₁ = -1

x₂ = 9+11/2

x₂ = 10

Odp. x₁ = -1  x₂ = 10

f) – x²+ 5x = 0 

Δ = 25

√Δ = 5

x₁ = -5 -5/-2

x₁ = 5

x₂ = -5 +5/-2

x₂ = 0

Odp. x₁ = 5 x₂ = 0

g)3x² + 12x = 0

Δ = 144

√Δ = 12

x₁ = -12 -12/6

x₁ = -4

x₂ = -12 +12/6

x₂ = 0

Odp. x₁ = -4 x₂ = 0

h)x² – 4 = 0

Δ =16

√Δ =4

x₁ = -4/2

x₁ = -2

x₂ = 4/2

x₂ = 2

Odp. x₁ = -2  x₂ = 2