muito urgente❗
QUESTÃO 07
Resolva as equações do 2º grau em R.
(A) x2 - 8x + 15 = 0
(B) x2 + 10x + 25 = 0
(C) x2 + 5x + 6 = 0
(D) x2 - 3x + 10 = 0
(E) -x2 + 12x - 20 = 0
(F) 3x2 + 4x + 1 = 0
(G) x2 - 7x + 12 = 0
(H) x2 + 5x + 4 = 0
Soluções para a tarefa
Resposta:
a) x² - 8x + 15 = 0 ➳ a = 1, b = -8, c = 15
» Calculo do Δ «
Δ = b² - 4 . a . c
Δ = (-8)² - 4 . 1 . 15
Δ = 64 - 4 . 1 . 15
Δ = 64 - 4 . 15
Δ = 64 - 60
Δ = 4
» Calculo do X «
X = -b ± √Δ / 2 . a
X = -(-8) ± √4 / 2 . 1
X = -(-8) ± 2 / 2 . 1
X = -(-8) ± 2 / 2
X = 8 ± 2 / 2 ➳ X' = 8 + 2 / 2 ➳ X' = 10 / 2 ➳ X' = 5
➳ X" = 8 - 2 / 2 ➳ X" = 6 / 2 ➳ X" = 3
➳ S = {5 , 3}
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b) x² + 10x + 25 = 0 ➳ a = 1, b = 10, c = 25
» Calculo do Δ «
Δ = b² - 4 . a . c
Δ = 10² - 4 . 1 . 25
Δ = 100 - 4 . 1 . 25
Δ = 100 - 4 . 25
Δ = 100 - 100
Δ = 0
» Calculo do X «
X = -b ± √Δ / 2 . a
X = -10 ± √0 / 2 . 1
X = -10 ± 0 / 2 . 1
X = -10 ± 0 / 2
X = -10 ± 0 / 2 ➳ X' = -10 + 0 / 2 ➳ X' = -10 / 2 ➳ X' = -5
➳ X" = -10 - 0 / 2 ➳ X" = -10 / 2 ➳ X" = -5
➳ S = {-5 , -5}
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c) x² + 5x + 6 = 0 ➳ a = 1, b = 5, c = 6
» Calculo do Δ «
Δ = b² - 4 . a . c
Δ = 5² - 4 . 1 . 6
Δ = 25 - 4 . 1 . 6
Δ = 25- 4 . 6
Δ = 25 - 24
Δ = 1
» Calculo do X «
X = -b ± √Δ / 2 . a
X = -5 ± √1 / 2 . 1
X = -5 ± 1 / 2 . 1
X = -5 ± 1 / 2
X = -5 ± 1 / 2 ➳ X' = -5 + 1 / 2 ➳ X' = -4 / 2 ➳ X' = -2
➳ X" = -5 - 1 / 2 ➳ X" = -6 / 2 ➳ X" = -3
➳ S = {-2 , -3}
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d) x² - 3x + 10 = 0 ➳ a = 1, b = -3, c = 10
» Calculo do Δ «
Δ = b² - 4 . a . c
Δ = (-3)² - 4 . 1 . 10
Δ = 9 - 4 . 1 . 10
Δ = 9 - 4 . 10
Δ = 9 - 40
Δ = -31
➳ S = {∉}, não existe raízes
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e) -x² + 12x - 20 = 0 ➳ a = -1, b = 12, c = -20
» Calculo do Δ «
Δ = b² - 4 . a . c
Δ = 12² - 4 . (-1) . (-20)
Δ = 144 - 4 . 1 . (-20)
Δ = 144 - (-4) . (-20)
Δ = 144 - (+80)
Δ = 144 - 80
Δ = 64
» Calculo do X «
X = -b ± √Δ / 2 . a
X = -12 ± √64 / 2 . 1
X = -12 ± 8 / 2 . 1
X = -12 ± 8 / 2
X = -12 ± 8 / 2 ➳ X' = -12 + 8 / 2 ➳ X' = -4 / 2 ➳ X' = -2
➳ X" = -12 - 8 / 2 ➳ X" = -20 / 2➳ X" = -10
➳ S = {-2 , -10}
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f) 3x² + 4x + 1 = 0 ➳ a = 3, b = 4, c = 1
» Calculo do Δ «
Δ = b² - 4 . a . c
Δ = 4² - 4 . 3 . 1
Δ = 16 - 4 . 3 . 1
Δ = 16 - 12 . 1
Δ = 16 - 12
Δ = 4
» Calculo do X «
X = -b ± √Δ / 2 . a
X = -3 ± √4 / 2 . 1
X = -3 ± 2 / 2 . 1
X = -3 ± 2 / 2
X = -3 ± 2 / 2 ➳ X' = -3 + 2 / 2 ➳ X' = -1/2
➳ X" = -3 - 2 / 2 ➳ X" = -5/2
➳ S = {-1/2 , -5/2}
================================================================
g) x² - 7x + 12 = 0 ➳ a = 1, b = -7, c = 12
» Calculo do Δ «
Δ = b² - 4 . a . c
Δ = (-7)² - 4 . 1 . 12
Δ = 49 - 4 . 1 . 12
Δ = 49 - 4 . 12
Δ = 49 - 48
Δ = 1
» Calculo do X «
X = -b ± √Δ / 2 . a
X = -(-7) ± √1 / 2 . 1
X = -(-7) ± 1 / 2 . 1
X = -(-7) ± 1 / 2
X = 7 ± 1 / 2 ➳ X' = 7 + 1 / 2 ➳ X' = 8 / 2 ➳ X' = 4
➳ X" = 7 - 1 / 2 ➳ X" = 6 / 2 ➳ X" = 3
➳ S = {4 , 3}
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h) x² + 5x + 4 = 0 ➳ a = 1, b = 5, c = 4
» Calculo do Δ «
Δ = b² - 4 . a . c
Δ = 5² - 4 . 1 . 4
Δ = 25 - 4 . 1 . 4
Δ = 25 - 4 . 4
Δ = 25 - 16
Δ = 9
» Calculo do X «
X = -b ± √Δ / 2 . a
X = -5 ± √9 / 2 . 1
X = -5 ± 3 / 2 . 1
X = -5 ± 3 / 2
X = -5 ± 3 / 2 ➳ X' = -5 + 3 / 2 ➳ X' = -2 / 2 ➳ X' = -1
➳ X" = -5 - 3 / 2 ➳ X" = -8 / 2 ➳ X" = -4
➳ S = {-1 , -4}