Determine as raizes reais destas equações do segundo grau.
(x+1)² = 16
5x²+ 10x=0
(x-1)²= 100
(a-3)²=36
10y²-200y=0
30b²+270b=0
(x+1)² = 16
5x²+ 10x=0
(x-1)²= 100
(a-3)²=36
10y²-200y=0
30b²+270b=0
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(x+1)² = 16(x + 1).(x + 1) = 16
x² + x + x + 1 = 16
x² + 2x + 1 - 16 =0
x² - 2x - 15 = 0
a = 1 b = - 2 c = - 15
Δ = b² - 4.a.c
Δ = (- 2)² - 4.(1).(-15)
Δ = 4 + 60
Δ = 64
x = - b ± √Δ
2.a
x = - (-2) ± √64
2.1
x = + 2 ± 8
2
x'= 2 + 8 = 10 = 5
2 2
x" = 2 - 8 = - 6 = - 3
2 2
S[- 3 , 5]
5x²+ 10x=0 ÷ (5)
x² + 2x = 0
x(x + 2) = 0
x= 0
(x+ 2) =
x + 2 = 0
x = - 2
S[- 2 , 0]
(x-1)²= 100
(x - 1).(x - 1) = 100
x² - x - x + 1 = 100
x² - 2x + 1 - 100
x² - 2x - 99 = 0
a = 1 b = - 2 c= - 99
Δ = b² - 4.a.c
Δ = (- 2)² - 4.(1).(-99)
Δ = 4 + 396
Δ = 400
x = - b ± √Δ
2.a
x = - (-2) ± √400
2.1
x = + 2 ± 20
2
x'= 2 + 20 = 22 = 11
2 2
x" = 2 - 20 = - 18 = - 9
2 2
S[- 9 , 11]
(a-3)²=36
(a - 3).(a -3) = 36
a² - 3a - 3a + 9 - 36 = 0
a² - 6a - 27 = 0
a = 1 b = - 6 c = - 27
Δ = b² - 4.a.c
Δ = (-6)² - 4.(1).(-27)
Δ = 36 + 108
Δ = 144
a= - b ± √Δ
2.a
a = - (-6) ± √144
2.1
a = + 6 ± 12
2
a'= 6 + 12 = 18 = 9
2 2
a" = 6 - 12 = - 6 = - 3
2 2
S[- 3 , 9]
10y²-200y=0 ÷ (10)
y² - 20y = 0
y(y - 20) = 0
y = 0
(y - 20) = 0
y - 20 = 0
y = + 20
S[0 , 20]
30b²+270b=0 ÷ (30)
b² + 9b = 0
b.(b + 9) = 0
b = 0
(b + 9) = 0
b + 9 = 0
b = - 9
S[- 9 , 0]