More Related Content Similar to Equção de 2º grau completa autor professor antonio carneiro (20) More from Antonio Carneiro (20) Equção de 2º grau completa autor professor antonio carneiro1. Professor de Matemática no Colégio Estadual Dinah Gonçalves
E Biologia na rede privada de Salvador-Bahia
Professor Antonio Carlos carneiro Barroso
email accbarroso@hotmail.com
Blog HTTP://ensinodematemtica.blogspot.com
Equações de 2º grau Completa:
−b+ ∆ −b
xi = e x i + x ii =
− b± ∆ 2a a
x= −b− ∆ c
2a x ii =
2a
x .x ii =
a
Resolvendo:
x 2 − +=
5x 6 0
a = 1
b = − 5
c = 6
∆b 2 −
= 4 ac
∆( 5 )
2
=− −1.6 = − =
4. 25 24 1
− b ± ∆
x =
2a
− 5)
(−± 1
x =
2.1
5 ± 1
x =
2
5 + 1 6
xi = = 3
2 2
5 − 1 4
x ii = = = 2
2 2
S = ,3)
( 2
2. x 2
− 15 =
8x + 0
a =
1
b =
−8
c =
15
∆ −
= 4 ac
b2
∆
=( 8) −
− 4.1.15
2
=
∆ − 4
= 60 =
64
− b ± ∆
x =
2a
x =
( 8)
− ± − 4
2. 1
8 ± 2
x =
2
8 + 2 10
xi = = =
5
2 2
8 −6 2
x ii = =3 =
2 2
S =( 5)
3,
X2-4x+4=0
▲=b2-4ac
▲=42-4.1.4=16-16=0
− ( − 4) ± 0
4±0 4+0 4 4−0 4
X= 2.1 x= x1 = = =2 x2 = = =2
2 2 2 2 2
S = ( 2)
x 2 + 2 x +1 = 0
−b ∆ − ( + 2) ± 0
∆ = b 2 − 4ac x= x=
2a 2.1
∆ = ( 2 ) − 4.1.1 = 4 − 4 = 0
2
−2 +0 −2
x1 = = = −1
2
−2 −0 −2
2
S = ( − 1)
x2 = = = −1
2 2
3. x 2 −4 x + =0
5
a = , b =− , c =5
1 4
∆=b 2 −4ac
∆=(−4 )
2
− .1.5 =
4 16 −20 =−4
∆0
〈
S =[ ]
x 2 −4 x − =0
5
a = , b =− , c =−
1 4 5
∆=b 2 −4ac
∆=(−4 ) −4.1.(− ) =
5 16 +20 =36
− ± ∆
b
x =
2a
−(−4 ) ± 36 4 ±6
x = =
2 .1 2
4 +6 10
x = = =5
2 2
4 −6 −2
x = = =− 1
2 2
S =(− ,5)
1
4x −4 x + =0
1
a =4, b =− , c =1
4
∆=b 2 −4ac =( −4 ) −4.4.1 =16 −
2
16 =0
−b ± ∆ −( −4 ) ± 0 4 ±0 4 1
x = = = = =
2a 2.4 8 8 2
1
S =
2
4. x 2 − x + = → = 2,3)
5 6 0 S (
x 2 − x + = → = 1,5 )
6 5 0 S (
x 2 − x − = → = − ,3)
2 3 0 S ( 1
x 2 − x − = → = − ,5 )
4 5 0 S ( 1
x 2 − x + = → = 1,6 )
7 6 0 S (
x2 − x +
7 10 = → = 2,5 )
0 S (
x 2 + x + = → = − ,− )
7 6 0 S ( 1 6
x2 − x + = → =
4 6 0 S [ ]
x 2 − x + = → = 1,2 )
3 2 0 S (
x 2 + x + = → (− ,− )
3 2 0 S 1 2
x 2 − x + = → = 2)
4 4 0 S (
x2 − x +
8 15 = → = 3,5)
0 S (
x2 − x +
9 14 = → = 2,7 )
0 S (
x2 −10 +25 = → = 5 )
0 S (
x2 + x +
11 30 = → = − ,− )
0 S ( 5 6
− 2 + x+
x 3 10 = → = 2,5)
0 S (
4
3 x 2 − x + = → = 1,
7 4 0 S
3
x2 + x −
4 21 = → = 3,− )
0 S ( 7
x2 + x +
8 16 = → = − )
0 S ( 4
3x 2 − x +
2 24 = → =
0 S [ ]
x2 − x +
10 24 = → = 4,6 )
0 S (
x 2 − x + = → = 1,3)
4 3 0 S (
x2 − x −
4 12 = → = − ,6 )
0 S ( 2
Professor Antonio Carlos Carneiro Barroso