Resolva as seguintes equações no conjunto IR
a) x² - 7x + 6 = 0
b) x² - x - 12 = 0
c) x² - 3x - 28 = 0
d) x² + 12x + 36 = 0
e) 6x² - x - 1 = 0
f) 9x² + 2x + 1 = 0
g) 3x² - 7x + 2 = 0
h) 25x² - 10 + 1 = 0
Soluções para a tarefa
∆ = b² - 4 . a . c
∆ = (- 7)² - 4 . 1 . 6
∆ = 49 - 24
∆ = 25
x = - b ± √∆/2 . a
x = - (- 7) ± √25/2 . 1
x = 7 ± 5/2
x' = 7 + 5/2
x' = 12/2
x' = 6
x'' = 7 - 5/2
x'' = 2/2
x' = 1
S = {1, 6}
______________________________
B) x² - x - 12 = 0
∆ = b² - 4 . a . c
∆ = (- 1)² - 4 . 1 . (- 12)
∆ = 1 + 48
∆ = 49
x = - b ± √∆/2 . a
x = - (- 1) ± √49/2 . 1
x = 1 ± 7/2
x' = 1 + 7/2
x' = 8/2
x' = 4
x'' = 1 - 7/2
x'' = - 6/2
x'' = - 3
S = {- 3, 4}
______________________________
C) x² - 3x - 28 = 0
∆ = b² - 4 . a . c
∆ = (- 3)² - 4 . 1 . (- 28)
∆ = 9 + 112
∆ = 121
x = - b ± √∆/2 . a
x = - (- 3) ± √121/2 . 1
x = 3 ± 11/2
x' = 3 + 11/2
x' = 14/2
x' = 7
x'' = 3 - 11/2
x'' = - 8/2
x'' = - 4
S = {- 4, 7}
______________________________
D) x² + 12x + 36 = 0
∆ = b² - 4 . a . c
∆ = 12² - 4 . 1 . 36
∆ = 144 - 144
∆ = 0
x = - b ± √∆/2 . a
x = - 12 ± √0/2 . 1
x = - 12 ± 0/2
x' = - 12 + 0/2
x' = - 12/2
x' = - 6
x'' = - 12 - 0/2
x'' = - 12/2
x'' = - 6
S = {- 6, - 6}
______________________________
E) 6x² - x - 1 = 0
∆ = b² - 4 . a . c
∆ = (- 1)² - 4 . 6 . (- 1)
∆ = 1 + 24
∆ = 25
x = - b ± √∆/2 . a
x = - (- 1) ± √25/2 . 6
x = 1 ± 5/12
x' = 1 + 5/12
x' = 6/12
x' = 0,5
x'' = 1 - 5/12
x'' = - 4/12
x'' = - 1/3
S = {- 1/3; 0,5}
______________________________
F) 9x² + 2x + 1 = 0
∆ = b² - 4 . a . c
∆ = 2² - 4 . 9 . 1
∆ = 4 - 36
∆ = - 32
Como o valor do delta (∆) é negativo, o cálculo termina aqui.
______________________________
G) 3x² - 7x + 2 = 0
∆ = b² - 4 . a . c
∆ = (- 7)² - 4 . 3 . 2
∆ = 49 - 24
∆ = 25
x = - b ± √∆/2 . a
x = - (- 7) ± √25/2 . 3
x = 7 ± 5/6
x' = 7 + 5/6
x' = 12/6
x' = 2
x'' = 7 - 5/6
x'' = 2/6
x'' = 1/3
S = {1/3, 2}
______________________________
H) 25x² - 10x + 1 = 0
∆ = b² - 4 . a . c
∆ = (- 10)² - 4 . 25 . 1
∆ = 100 - 100
∆ = 0
x = - b ± √∆/2 . a
x = - (- 10) ± √0/2 . 25
x = 10 ± 0/50
x' = 10 + 0/50
x' = 10/50
x' = 0,2
x'' = 10 - 0/50
x'' = 10/50
x'' = 0,2
S = {0,2; 0,2}
Resposta:
A) x² - 7x + 6 = 0
∆ = b² - 4 . a . c
∆ = (- 7)² - 4 . 1 . 6
∆ = 49 - 24
∆ = 25
x = - b ± √∆/2 . a
x = - (- 7) ± √25/2 . 1
x = 7 ± 5/2
x' = 7 + 5/2
x' = 12/2
x' = 6
x'' = 7 - 5/2
x'' = 2/2
x' = 1
S = {1,
B) x² - x - 12 = 0
∆ = b² - 4 . a . c
∆ = (- 1)² - 4 . 1 . (- 12)
∆ = 1 + 48
∆ = 49
x = - b ± √∆/2 . a
x = - (- 1) ± √49/2 . 1
x = 1 ± 7/2
x' = 1 + 7/2
x' = 8/2
x' = 4
x'' = 1 - 7/2
x'' = - 6/2
x'' = - 3
S = {- 3, 4}
C) x² - 3x - 28 = 0
∆ = b² - 4 . a . c
∆ = (- 3)² - 4 . 1 . (- 28)
∆ = 9 + 112
∆ = 121
x = - b ± √∆/2 . a
x = - (- 3) ± √121/2 . 1
x = 3 ± 11/2
x' = 3 + 11/2
x' = 14/2
x' = 7
x'' = 3 - 11/2
x'' = - 8/2
x'' = - 4
S = {- 4, 7}
D) x² + 12x + 36 = 0
∆ = b² - 4 . a . c
∆ = 12² - 4 . 1 . 36
∆ = 144 - 144
∆ = 0
x = - b ± √∆/2 . a
x = - 12 ± √0/2 . 1
x = - 12 ± 0/2
x' = - 12 + 0/2
x' = - 12/2
x' = - 6
x'' = - 12 - 0/2
x'' = - 12/2
x'' = - 6
S = {- 6, - 6}
E) 6x² - x - 1 = 0
∆ = b² - 4 . a . c
∆ = (- 1)² - 4 . 6 . (- 1)
∆ = 1 + 24
∆ = 25
x = - b ± √∆/2 . a
x = - (- 1) ± √25/2 . 6
x = 1 ± 5/12
x' = 1 + 5/12
x' = 6/12
x' = 0,5
x'' = 1 - 5/12
x'' = - 4/12
x'' = - 1/3
S = {- 1/3; 0,5}
F) 9x² + 2x + 1 = 0
∆ = b² - 4 . a . c
∆ = 2² - 4 . 9 . 1
∆ = 4 - 36
∆ = - 32
Como o valor do delta (∆) é negativo, o cálculo termina aqui.
G) 3x² - 7x + 2 = 0
∆ = b² - 4 . a . c
∆ = (- 7)² - 4 . 3 . 2
∆ = 49 - 24
∆ = 25
x = - b ± √∆/2 . a
x = - (- 7) ± √25/2 . 3
x = 7 ± 5/6
x' = 7 + 5/6
x' = 12/6
x' = 2
x'' = 7 - 5/6
x'' = 2/6
x'' = 1/3
S = {1/3, 2}
H) 25x² - 10x + 1 = 0
∆ = b² - 4 . a . c
∆ = (- 10)² - 4 . 25 . 1
∆ = 100 - 100
∆ = 0
x = - b ± √∆/2 . a
x = - (- 10) ± √0/2 . 25
x = 10 ± 0/50
x' = 10 + 0/50
x' = 10/50
x' = 0,2
x'' = 10 - 0/50
x'' = 10/50
x'' = 0,2
S = {0,2; 0,2}
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