Question

resolva as seguintes esquaçoes do 2 grau,sendo U=R:

a)
$x - 5x = 0$
b)
$x - 100 = 0$
c)
$x - 7x - 30 = 0$
d)
$2x + 5x - 3 =$

Answer 1

Olá!!!

Resolução!!!

a)
x² - 5x = 0
x • ( x - 5 ) = 0
x' = 0

x - 5 = 0
x" = 5

S = { 0, 5 }

b)
x² - 100 = 0
x² = 100
x = ± √100
x = ± 10
x' = 10
x" = - 10

S = { - 10, 10 }

c)
x² - 7x - 30 = 0

a = 1, - 7, c = - 30

∆ = b² - 4ac
∆ = ( - 7 )² - 4 • 1 • ( - 30 )
∆ = 49 + 120
∆ = 169

x = - b ± √∆ /2a
x = - ( - 7 ) ± √169 / 2 • 1
x = 7 ± 13/2
x' = 7 + 13/2 = 20/2 = 10
x" = 7 - 13/2 = - 6/2 = - 3

S = { - 3, 10 }

d)
2x² + 5x - 3 = 0

a = 2, b = 5, c = - 3

∆ = b² - 4ac
∆ = 5² - 4 • 2 • ( - 3 )
∆ = 25 + 24
∆ = 49

x = - b ± √∆ / 2a
x = - 5 ± √49 / 2 • 2
x = - 5 ± 7 / 4
x' = - 5 + 7 /4 = 2/4 : 2 = 1/2
x" = - 5 - 7 /4 = - 12/4 = - 3

S = { - 3, 1/2 }

Espero ter ajudado!!!