Respostas

2014-05-31T15:31:09-03:00
Olá, Leeh199915!

a)
x² - 14x + 49 = 0
a = 1
b = -14
c = 49
Δ = b² -4ac
Δ = (-14)² - 4.1.49
Δ = 196 - 196
Δ = 0
-b / 2a
- (-14) / 2.1
14 / 2
7

b) 
y² - 18y + 72 = 0
a = 1
b = -18
c = 72
Δ = b² -4ac
Δ = (-18)² - 4.1.72
Δ = 324 - 288
Δ = 36

-b +- raiz de delta / 2.a
-(-18) +- raiz de 36 / 2.1
18 +- 6 / 2

x' = 18 - 6/2 = 12/2 = 6
x'' = 18 + 6/2 = 24/2 = 12

c) t² + 2t - 3 = 0
a = 1
b = 2
c = -3
Δ = b² - 4ac
Δ = 2² - 4.1.(-3)
Δ = 4 + 12
Δ = 16

-b +- raiz de delta /  2.a
-2 +- raiz de 16 / 2.1
-2 +- 4/2

x' = -2 + 4/2 = 2/2 = 1
x'' = -2 - 4/2 = -8/2 = -4

d) 4x² + 12x + 5 = 0
a = 4
b = 12
c = 5
Δ = b² - 4ac
Δ = 12² - 4.4.5
Δ = 144 - 80
Δ =  64

-b +- raiz de delta / 2a
-12 +- raiz de 64 / 2.1
-12 +- 8/2

x' = -12 + 8/2 = -4/2 = -2
x'' = -12 - 8/2 = -20/2 = -10

e) 9x² + 12x - 5 = 0
a = 9
b = 12
c = -5
Δ = b² - 4ac
Δ = 12² -4.9.(-5)
Δ = 144 + 180
Δ = 324

-b +- raiz de delta / 2a
-12 +- raiz de 324 / 2.9
-12 +- 18/18

x' = -12 + 18/18 = 6/18 (simplificaremos)
6:6 = 1
18:6 = 3
x' = 1/3
x'' = -12 - 18/18 = -30/18 (simplificaremos)
30:3 = 10
18:3 = 6

10:2 = 5
6:2 = 3
x'' = 5/3

2 3 2