Professor Antonio Carlos Carneiro Barroso teaches mathematics at Colégio Estadual Dinah Gonçalves and biology at a private school in Salvador, Bahia. He provides solutions to various quadratic equations in one variable, finding the roots and listing the solutions. He gives the steps for solving the equations, including finding the discriminant and using the quadratic formula.

1. 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:
x2 − x + =
5 6 0
a =1
b = 5
−
c =6
∆ b 2 − ac
= 4
∆ (− )
2
= 5 − .1 .6 =
4 25 −24 =1
− ± ∆
b
x =
2a
−− ) ± 1
( 5
x =
2 .1
5± 1
x =
2
i 5 + 1 6
x = = 3
2 2
5− 1 4
x ii = = = 2
2 2
S = 2,3)
(

2. x2 − + =
8x 15 0
a =1
b =−
8
c =
15
∆b 2 −
= 4 ac
∆ ( 8 ) − 1.15 =
2
= − 4.
∆ 64 − =
= 60 4
−±∆
b
x =
2a
− 8 )±4
(−
x =
2.1
8 ± 2
x =
2
8 + 2 10
xi = = =5
2 2
8 − 2 6
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