Respostas
Resposta:
a) x² -6x + 8 = 0
Δ = b² -4.a.c
Δ = -6² - 4.1.8
Δ = 36 - 32
Δ = 4
x = ( - )– 6 ± √4
2·1
x = 6 ± 2
2
x' = 6 + 2 >> x' = 8/2 >> x' = 4
2
x'' = 6 - 2 >> x'' = 4/2 >> x'' = 2
2
b) x² - 8x + 15 = 0
Δ = b² -4.a.c
Δ = -8² - 4.1.15
Δ = 64 - 60
Δ = 4
x = -(-b) ± √Δ
2.a
x = 8 ± √4
2.1
x = 8 ± 2
2
x' = 8+2 >> x' = 10/2 >> x' = 5
2
x'' = 8-2 >> x'' = 6/2 >> x'' = 3
2
c) x² - 7x + 6 = 0
Δ = -7² - 4.1.6
Δ = 49 - 24
Δ = 25
x = -(-7) +- √25
2.1
x = 7 +- 5
2
x' = 7 + 5 >> x' = 12/2 >> x' = 6
2
x'' = 7-5 >> x'' = 2/2>> x'' = 1
2
d) x² + 2x + 12 = 0
Δ = 2² - 4.1.12
Δ = 4 - 48
Δ = -44
x = -(+2) +- √-44
2.1
x' = -2 + 12i >> x' = -1 + 6i
2
x'' = -2 - 12i >> x'' = -1 -6i
2
e) x² + 10x - 25 = 0
Δ = 10² -4.1.(-25)
Δ = 100 + 100
Δ = 200
x = -10 +- √200
2.1
x' = - 10 + √200
2
x'' = -10 - √200
2
f) x² - 2x + 13 = 0
Δ = (-2)² - 4.1.13
Δ = 4 - 52
Δ = -48
x = 2 +- √-48
2.1
x' = 2 +4i√3 >> x' = 1 + 2i √3
2
g) x² + 4x + 4 = 0
Δ = 4² - 4.1.4
Δ = 16 - 16
Δ = 0
x = (-) +4 +- √0
2.1
x' = -4 >> x' -4/2 >> x' = -2
2
x'' = -4 >> x'' = -2
2
h) x² - 13x +36 = 0
Δ = (-13)² - 4.1.36
Δ = 169 -144
Δ = 25
x = 13 +- √25
2.1
x' = 13 + 5 >> x' = 18/2 >> x' = 9
2
x'' = 13 - 5 >> x'' = 8/2 >> x'' = 4
2
2) x² -3x +4 = 0
Δ = (-3)² -4.1.4
Δ = 9 - 16
Δ = -7
x = 3 +- √-7
2.1
x' = 3 + 7i
2
x'' = 3 - 7i
2
3) x² - 6x + 5 = 0
Δ = (-6)² - 4.1.5
Δ = 36 - 20
Δ = 16
x = 6 +- √16
2.1
x' = 6 + 4 >> x' = 10/2 >> x' = 5
2
x'' = 6-4 >> x'' = 2/2 >> x'' = 1
2
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