Question

Resolva as equações de 2 grau, encontrado suas raízes:
a) X^2+3X=0
b)X^2=3
c)X^2-9X+18=0
d)X^2-3X=18
e)X^2-9=0
f) 2X^2-2X=24

Answer 1

a) x² + 3x = 0
x(x+ 3)= 0
x= 0
x+ 3= 0
x= - 3
x= (0 , - 3)

b) x²= 3x
x²- 3x=0
x (x-3)=0
x = 0
x-3=0
x= 3

c)x² -9x+18=0
a= 1; b= -9 ; c=18
∆ = b² - 4 . a . c
∆ = (-9)² - 4 . (1) . (18)
∆ = 81- 72
∆ = 9
x = - (-9) ± √9) / 2.(1)
x = 9 ± 3/ 2

x'= 9+ 3/ 2 = 12/2
x'= 6

x"= 9 - 3/ 2 = 6/2
x"= 3


d) x² -3x=18
x²-3x-18=0
a= 1 ; b= -3 ; c= -18
∆ = b² - 4 . a . c
∆ = (-3)² - 4 . (1) . (-18)
∆ = 9+72
∆ = 81
x = -(-3) ± √81) / 2.(1)
x = 3 ± 9/ 2

x'= 3 + 9/ 2 = 12/2
x'= 6

x"= 3 - 9/ 2 = - 6/2
x"= -3


e) x²-9=0
x²=9
x=√9
x= ± 3

f) 2x²-2x=24
2x²-2x-24=0
a= 2 ; b= -2 ; c= -24
∆ = b² - 4 . a . c
∆ = (-2)² - 4.(2).(-24)
∆ = 4+192
∆ = 196
x = -(-2)± √196) / 2.(2)
x = 2 ± 14/4

x'= 2+ 14/4 = 16/4
x'= 4

x"= 2 -14/4 = 12/4
x"= 3