Question

resolva as equações de 2 grau:
a) x² - 8x + 12=0
b) 2x² + 7x +3=0
c) x² - 4x + 3=0
d) -x² + x +2=0

Answer 1

a)X^2 - 8x+12=0
X^2-2x-6x+12=0
x^x(x-2) -6 (x-2)=0
(x-2)×(x-6) =0
x-2=0
x-6=0
X1=2
X2=6

b)2x^2 +7x+3=0
2x^2+6x+x+3=0
2x × (x+3)+x+3=0
(x+3) × (2x+1)=0
x+3=0
2x + 1=0

X1= -3
X2=1/2

C)X^2 - 4x + 3=0
x^2-x-3x+3=0
X ×(x-1)-3( x-1)=0
(X-1) × (X-3)=0
x-1=0
x-3=0

x1= 1
x2=3

d)-x^2+x+2=0
x^2-x-2=0
x^2 + x - 2x-2=0
x × (x+1) × ( x-2)=0
x+1=0
x-2=0

X1= -1
X2= 2

Answer 2

Vamos lá

Calculo:

Resolvendo a letra A

X² - 8X + 12 = 0

Os coeficientes

A = 1

B = - 8

C = 12

Δ = b² - 4 • a • c

Δ = ( - 8 )² - 4 • 1 • 12

Δ = 64 - 48

Δ = 16

X = - b ± √ Δ / 2 • a

X = 8 ± √ 16 / 2 • 1

X = 8 ± 4 / 2

X1 = 8 + 4 / 2 = 12 / 2 = 6

X2 = 8 - 4 / 2 = 4 / 2 = 2

S { 6 , 2 }

RESOLVENDO A LETRA B

2X² + 7X + 3 = 0

Os coeficientes

A = 2

B = 7

C = 3

Δ = b² - 4 • a • c

Δ = 7² - 4 • 2 • 3

Δ = 49 - 24

Δ = 25

X = - b ± √ Δ / 2 • a

X = - 7 ± √ 25 / 2 • 2

X = - 7 ± 5 / 4

X1 = - 7 + 5 / 4 = - 2 / 4 = - 1 / 2

X2 = - 7 - 5 / 4 = - 12 / 4 = - 3

S { - 1 / 2 , - 3 }

RESOLVENDO A LETRA C

X² - 4X + 3 = 0

Os coeficientes

A = 1

B = - 4

C = 3

Δ = b² - 4 • a • c

Δ = ( - 4 )² - 4 • 1 • 3

Δ = 16 - 12

Δ = 4

X = - b ± √ Δ / 2 • a

X = 4 ± √ 4 / 2 • 1

X = 4 ± 2 / 2

X1 = 4 + 2 / 2 = 6 / 2 = 3

X2 = 4 - 2 / 2 = 2 / 2 = 1

S { 3 , 1 }

RESOLVENDO A LETRA D

- X² + X + 2 = 0

Os coeficientes

A = - 1

B = 1

C = 2

Δ = b² - 4 • a • c

Δ = 1² - 4 • ( - 1 ) • 2

Δ = 1 + 8

Δ = 9

X = - b ± √ Δ / 2 • a

X = - 1 ± √ 9 / 2 • ( - 1 )

X = - 1 ± 3 / - 2

X1 = - 1 + 3 / - 2 = 2 / - 2 = - 1

X2 = - 1 - 3 / 2 = - 4 / - 2 = 2

S { - 1 , 2 }