Question

Rozwiąż równiania kwadratowe:

a) x² + 4x - 5 = 0

b) -x² + 4x + 21 = 0

c) 2x² + 5x - 12 = 0

d) 3x² + 7x - 20 = 0

Answer 1

a) x² + 4x - 5 = 0
a = 1, b = 4, c = -5

Δ = b² - 4ac
Δ = 4² - 4 * 1 * (-5)
Δ = 16 -(-20)
Δ = 36
Δ = √36
Δ = 6

x₁ = -b - √Δ / 2a
x₁ = -4 - 6 / 2 * 1
x₁ = -10 / 2
x₁ = -5

x₂ = -b + √Δ / 2a
x₂ = -4 + 6 / 2
x₂ = 2 / 2
x₂ = 1
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b) -x² + 4x + 21 = 0
a = -1, b = 4, c = 21

Δ = b² - 4ac
Δ = 4² - 4 * (-1) * 21
Δ = 16 -(-84)
Δ = 100
Δ = √100
Δ = 10

x₁ = -b - √Δ / 2a
x₁ = -4 - 10 / 2 * (-1)
x₁ = -14 / -2
x₁ = 7

x₂ = -b + √Δ / 2a
x₂ = -4 + 10 / 2 * (-1)
x₂ = 6 / -2
x₂ = -3
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c) 2x² + 5x - 12 = 0
a = 2, b = 5, c = -12

Δ = b² - 4ac
Δ = 5² - 4 * 2 * (-12)
Δ = 25 -(-96)
Δ = 121
Δ = √121
Δ = 11

x₁ = -b - √Δ / 2a
x₁ = -5 - 11 / 2 * 2
x₁ = -16 / 4
x₁ = -4

x₂ = -b + √Δ / 2a
x₂ = -5 + 11 / 2 * 2
x₂ = 6 / 4
x₂ = 1,5
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d) 3x² + 7x - 20 = 0
a = 3, b = 7, c = -20

Δ = b² - 4ac
Δ = 7² - 4 * 3 * (-20)
Δ = 49 -(-240)
Δ = 289
Δ = √289
Δ = 17

x₁ = -b - √Δ / 2a
x₁ = -7 - 17 / 2 * 3
x₁ = -24 / 6
x₁ = -4

x₂ = -b + √Δ / 2a
x₂ = -7 + 17 / 2 * 3
x₂ = 10 / 6
x₂ = 1 i 4/6
x₂ = 1 i 2/3

Answer 2

D(delta) =b^2 -4ac

x1 =(-b-VD):2a

x2 =(-b+VD):2a

 

a)

x2 +4x-5 =0

D =16+20 =36

VD =V36

VD =6

x1 =(-4-6):2 = -5

x2 =(-4+6):2 =1

b)

-x2 +4x +21 =0

D =16+84 =100

VD =10

x1 =(-4-10):(-2) = 7

x2 =(-4+10):(-2) = -3

c)

2x2 +5x -12 = 0

D =25+96 =121

VD =11

x1 =(-5-11):4 = -4

x2 =(-5+11):4 =3/2 =1,5

d)

3x2 +7x -20 = 0

D =49+240 =289

VD =17

x1 =(-7-17):6 = -4

x2 =(-7+17):6 =5/3 =1 i 2/3