2) Determine as raízes reais das equações incompletas.
a) x2 – 5x = 0
b) -x + 12x = 0
c) 5x + x = 0
d) x2 - 9x = 0
e) x2 - 9 = 0
f) 25x2 – 1 = 0
g) x - 64 = 0
h) -7x' + 28 = 0
Respostas
Resposta:
a) x² - 5x = 0
A = 1 B = - 5 C = 0
delta = (-5)² - 4. 1 .0
delta = 25 - 0
delta = 25
x = -(-5) + ou - √25 / 2 . 1
x = 5 + ou - 5 / 2
x' = 5 + 5 / 2
x' = 10 / 2
x' = 5
x" = 5 - 5 / 2
x" = 0 / 2
x" = 0
b) - x² + 12x = 0
A = - 1 B = 12 C = 0
delta = 12² - 4 . (-1) . 0
delta = 144 - 0
delta = 144
x = - 12 + ou - √144 / 2 . (-1)
x = - 12 + ou - 12 / (-2)
x' = - 12 + 12 / (-2)
x' = 0 / (-2)
x' = 0
x" = - 12 - 12 / (-2)
x" = - 24 / (-2)
x" = 12
c) 5x² + x = 0
A = 5 B = 1 C = 0
delta = 1² - 4 . 5 . 0
delta = 1 - 0
delta = 1
x = - 1 + ou - √1 / 2 . 5
x = - 1 + ou - 1 / 10
x' = - 1 + 1 / 10
x' = 0 / 10
x' = 0
x" = - 1 - 1 / 10
x" = - 2 / 10 : 2
x" = - 1 / 5
d) x² - 9x = 0
A = 1 B = - 9 C = 0
delta = (-9)² - 4 . 1 . 0
delta = 81 - 0
delta = 81
x = -(-9) + ou - √81 / 2 . 1
x = 9 + ou - 9 / 2
x' = 9 + 9 / 2
x' = 18 / 2
x' = 9
x" = 9 - 9 / 2
x" = 0 / 2
x" = 0
e) x² - 9 = 0
A = 1 B = 0 C = - 9
delta = 0² - 4 . 1 . (-9)
delta = 0 + 36
delta = 36
x = 0 + ou - √36 / 2 . 1
x = 0 + ou - 6 / 2
x' = 0 + 6 / 2
x' = 6 / 2
x' = 3
x" = 0 - 6 / 2
x" = - 6 / 2
x" = - 3
f) 25x² - 1 = 0
A = 25 B = 0 C = - 1
delta = 0² - 4 . 25 . (-1)
delta = 0 + 100
delta = 100
x = 0 + ou - √100 / 2 . 25
x = 0 + ou - 10 / 50
x' = 0 + 10 / 50
x' = 10 / 50 : 10
x' = 1 / 5
x" = 0 - 10 / 50
x" = - 10 / 50 : 10
x" = - 1 / 5
g) x² - 64 = 0
A = 1 B = 0 C = - 64
delta = 0² - 4 . 1 . (-64)
delta = 0 + 256
delta = 256
x = 0 + ou - √256 / 2 . 1
x = 0 + ou - 16 / 2
x' = 0 + 16 / 2
x' = 16 / 2
x' = 8
x" = 0 - 16 / 2
x" = - 16 / 2
x" = - 8
h) - 7x² + 28 = 0
A = - 7 B = 0 C = 28
delta = 0² - 4 . (-7) . 28
delta = 0 + 784
delta = 784
x = 0 + ou - √784 / 2 . (-7)
x = 0 + ou - 28 / (-14)
x' = 0 + 28 / (-14)
x' = 28 / (-14)
x' = - 2
x" = 0 - 28 / (-14)
x" = - 28 / (-14)
x" = 2