Question

Calcule as raízes das equações:
a)x2 +5x+6
b)9x2 –12x+4
c)x2 -3x–10 d)x2 +x–2
e)x2 –4x
f)x2-56
g)x2 -144
h)2x2 +6x

Answer 1

a) x^2 + 5x + 6 = 0

a = 1

b = 5

c = 6

Δ = b^2 - 4 . a . c

Δ  = 5^2 - 4 . 1 . 6

Δ = 25 - 4 . 6

Δ = 25 - 24

Δ = 1

x = -b ± √Δ /2 . a

x = -5 ± √1 /2 . 1

x = -5 ± 1 /2

x' = -5 - 1 /2

x' = -6/2

x' = -3

x" = -5 + 1 /2

x" = -4/2

x" = -2

b) 9x^2 - 12x + 4 = 0

a = 9

b = -12

c = 4

Δ = b^2 - 4 . a . c

Δ  = (-12)^2 - 4 . 9 . 4

Δ = 144 - 16 . 9

Δ = 144 - 144

Δ = 0

x = -b ± √Δ /2 . a

x = -(-12) ± √0 /2 . 9

x = 12 ± 0 /18

x' = 12 - 0 /18

x' = 12/18

x' = 6/9

x" = 12 + 0 /18

x" = 12/18

x" = 6/9

c) x^2 - 3x - 10 = 0

a = 1

b = -3

c = -10

Δ = b^2 - 4 . a . c

Δ  = (-3)^2 - 4 . 1 . (-10)

Δ = 9 - (-40)

Δ = 9 + 40

Δ = 49

x = -b ± √Δ /2 . a

x = -(-3) ± √49 /2 . 1

x = 3 ± 7 /2

x' = 3 - 7 /2

x' = -4/2

x' = -2

x" = 3 + 7 /2

x" = 10/2

x" = 5

d) x^2 + x - 2 = 0

a = 1

b = 1

c = -2

Δ = b^2 - 4 . a . c

Δ  = 1^2 - 4 . 1 . (-2)

Δ = 1 - (-8)

Δ = 1 + 8

Δ = 9

x = -b ± √Δ /2 . a

x = -1 ± √9 /2 . 1

x = -1 ± 3 /2

x' = -1 - 3 /2

x' = -4/2

x' = -2

x" = -1 + 3 /2

x" = 2/2

x" = 1

e) x^2 - 4x = 0

x . (x - 4) = 0

x' = 0

x - 4 = 0

x = 4

x" = 4

f) x^2 - 56 = 0

x^2 = 56

x = √56

x = ± √56

x' = -√56

x" = √56

g) x^2 - 144 = 0

x^2 = 144

x = √144

x = ±12

x' = -12

x" = 12

h) 2x^2 + 6x = 0

x . (2x + 6) = 0

x' = 0

2x + 6 = 0

2x = -6

x = -6/2

x = -3

x" = -3