Question

Resolver as seguintes equações do 2° grau, identifique os coeficientes e determine as raízes se existir. A) X² - 5× + 6= 0
B) x² - 8× + 12 = 0
C) x²+ 2× - 8= 0

Answer 1

A) x² -5x +6 
Coeficientes:
a = 1
b = -5
c = 6

Δ= b² -4ac
Δ= (-5)² -4.1.6
Δ= 25 - 24
Δ= 1

Raízes reais:
x= -b +/- √Δ / 2a
x= -(-5) +/- √1 / 2.1
x'= 5 +1 /2
x'= 6/2
x'= 3

x''= 5 -1/2
x''= 4/2
x''= 2

B)x² -8x +12
Coeficientes:
a = 1
b = -8
c = 12

Δ= b² -4ac
Δ= (-8)² -4.1.12
Δ= 64 -48
Δ= 16

Raízes reis:
x= -b +/- √Δ / 2a
x= -(-8) +/- √16 / 2.1
x'= 8 +4 / 2
x'= 12/2
x'= 6

x''= 8 -4 /2
x''= 4 /2
x''= 2

C)x² +2x -8
Coeficientes:
a = 1
b = 2
c = -8

Δ= b² -4ac
Δ= 2² -4.1.(-8)
Δ= 4 + 32
Δ= 36

Raízes reais:
x= -b +/- √Δ / 2a
x= -2 +/- √36 / 2.1
x'= -2 +6 /2
x'= 4 /2
x'= 2

x''= -2 -6/ 2
x''= -8/2
x''= -4

Bons estudos!

Answer 2

a)
x² - 5x + 6 = 0
Coeficientes: a = 1; b = - 5, c = 6

Δ = b² - 4ac
Δ = (-5)² - 4.1.6
Δ = 25 -24
Δ = 1

x = - b +/- √Δ = - (-5) +/- √1         
          2a                2.1

x = 5 + 1 = 6/2 = 3
         2

x = 5 - 1 = 4/2 = 2
        2
R.: x = 3 e x = 2
_________________________________________
b)
x² - 8x + 12 = 0
Coeficientes:  a = 1; b = - 8; c = 12

Δ = b² - 4ac
Δ = (-8)² - 4.1.12
Δ = 64 - 48
Δ = 16

x = - b +/- √Δ = - (-8) +/- √16       
           2a                     2.1

x = 8 + 4 = 12/2 = 6
         2

x = 8 - 4 = 4/2 = 2
        2

Resp.: x = 6 e x = 2
________________________________________
x² + 2x - 8 = 0
Coeficientes: a = 1; b = 2; c = - 8

Δ = b² - 4ac
Δ = 2² - 4.1.(-8)
Δ = 4 + 32
Δ = 36

x = - b +/- √Δ = - 2 +/- √36
          2a                2.1

x' = - 2 + 6 = 4/2 = 2
          2

x" = - 2 - 6 = -8/2 = - 4
           2

R.: x = 2 e x = - 4