Ache As Raízes Das Equações:
A) X²-X-20=0
B)X²-3X-4=0
C)X²-8X+7=0
D)X²-14X48=0
E)X²5X+5=0
G)X²+3X-28=O
H)X²+3X-28=0
I)-X²+X+12=0
J)-X²+X+12=0
K)-X²+6X-5=0
L)6X²-X-5=0
M)25X²-2X=-4
N)2X=15-X²
O)X²+3X-6=-8
P)(X+3)²=1
Q)X(X+3)-40=0
R)-X²+X+30=0
S)(X-5)² = 1
T)X²+3X-28=0
VALENDO TODOS OS MEUS PONTOS!!!
Soluções para a tarefa
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x = [-b +- √Δ]/2.a
Δ = b² - 4ac
A) X²-X-20=0
Δ = (-1)² - 4.1(-20) = 1 + 80 = 81
x = [-(-1) +- √81]/2.1
x' = (1+9)/2 = 10/2 = 5
x" = (1-9)/2 = 8/2 = 4
B)X²-3X-4=0
Δ = (-3)² - 4.1.(-4) = 9 + 16 = 25
x = [-(-3) +- √25]/2.1
x' = (3 + 5)/ 2 = 8/2 = 4
x" = (3 - 5)/2 = -2/2 = -1
C)X²-8X+7=0
Δ = (-8)² - 4.1.7 = 64 - 28 = 36
x = [-(-8) +- √36]/2.1
x' = (8 + 6)/2 = 14/2 = 7
x" = (8 - 6)/2 = 2/2 = 1
D)X²-14X+ 48=0
Δ = (-14)² - 4.1.48 = 196 - 192 = 4
x = [-(-14) +- √4]/2.1
x' = (14 + 2)/2 = 16/2 = 8
x" = (14 - 2)/2 = 12/2 = 6
E)X²+5X+5=0
Δ = 5² - 4.1.5 = 25 - 20 = 5
x = [-5 +- √5]/2.1
x' = (-5 + √5)/2
x" = (-5 - √5)/2
G)X²+3X-28=O
Δ = 3² - 4.1.(-28) = 9 + 112 = 121
x = [-3 +- √121]/2.1
x' = (-3 + 11)/2 = 8/2 = 4
x" = (-3 - 11)/2 = -14/2 = -7
H)X²+3X-28=0
Δ = 3² - 4.1.(-28) = 9 + 112 = 121
Idem ao anterior.
I)-X²+X+12=0
Δ = 1² - 4.(-1).12 = 1 + 48 = 49
x = [-1 +- √49]/2.(-1)
x' = (-1 + 7)/(-2) = 6/(-2) = -3
x" = (-1 - 7)/(-2) = (-8)/(-2) = 4
J)-X²+X+12=0
Δ = 1² - 4.(-1).12 = 1 + 48 = 49
Idem ao anterior.
K)-X²+6X-5=0
Δ = 6² -4.(-1).(-5) = 36 -20 = 16
x = [-6 +- √16]/2.(-1)
x' = (-6 + 4)/(-2) = -2/(-2) = 1
x" = (-6 - 4)/(-2) = -10/(-2) = 5
L)6X²-X-5=0
Δ = (-1)² - 4.6.(-5) = 1 + 120 = 121
x = [-(-1) +- √121]/2.6
x' = [1 + 11]/12 = 12/12 = 1
x" =(1 - 11)/12 = -10/12 = -5/6
M)25X²-2X=-4
25x² - 2x + 4 = 0
Δ = (-2)² - 4.25.4 = 4 - 400 = -396
x = [-(-2) +- √-396]/2.25
x = [ 2 +- √-396]/50 --------- Solução no conjunto de Número Complexos
N) 2X=15-X²
x² + 2x - 15 = 0
Δ = 2² - 4.1.(-15) = 4 + 60 = 64
x = [-2 +- √64]/2.1
x' = (-2 + 8)/2 = 6/2 = 3
x" = (-2 - 8)/2 = -10/2 = -5
O)X²+3X-6=-8
x² + 3x - 6 + 8 = 0
x² + 3x + 2 = 0
Δ = 3² - 4.1.2 = 9 - 8 = 1
x = [-3 +- √1]/2.1
x' = (-3 + 1)/2 = -2/2 = -1
x" = (-3 -1)/2 = -4/2 = -2
P)(X+3)²=1
x² + 2x3 + 9 = 1
x² + 6x + 9 - 1 = 0
x² + 6x + 8 = 0
Δ = 6² - 4.1.8 = 36 - 32 = 4
x = [-6 +- √4]/2.1
x' = (-6 + 2)/2 = -4/2 = -2
x" = (-6 - 2)/2 = -8/2 = -4
Q)X(X+3)-40=0
x² + 3x - 40 = 0
Δ = 3² - 4.1.(-40) = 9 + 160 = 169
x = [-3 +- √169]/2.1
x' = (-3 + 13)/2 = 10/2 = 5
x" = (-3 - 13)/2 = -16/2 = -8
R)-X²+X+30=0
Δ = 1² - 4.(-1).30 = 121
x = [-1 +- √121]/2.(-1)
x' = [-1 + 11]/(-2) = 10/(-2) = -5
x" = [-1 - 11]/(-2) -12/(-2) = 6
S)(X-5)² = 1
x² + 2x5 + 25 - 1 = 0
x² + 10x + 24 = 0
Δ = 10² - 4.1.24 = 100 - 96 = 4
x = [-10 +- √4]/2.1
x' = -10 + 2/2 = -8/2 = -4
x" = -10 - 2/2 = -12/2 = -6
T)X²+3X-28=0
Δ = 3² - 4.1.(-28) = 9 + 112 = 121
x = [-3 +- √121]/2.1
x' = -3 + 11/2 = 8/2 = 4
x" = -3 - 11/2 = -14/2 = -7
Espero ter ajudado.
Δ = b² - 4ac
A) X²-X-20=0
Δ = (-1)² - 4.1(-20) = 1 + 80 = 81
x = [-(-1) +- √81]/2.1
x' = (1+9)/2 = 10/2 = 5
x" = (1-9)/2 = 8/2 = 4
B)X²-3X-4=0
Δ = (-3)² - 4.1.(-4) = 9 + 16 = 25
x = [-(-3) +- √25]/2.1
x' = (3 + 5)/ 2 = 8/2 = 4
x" = (3 - 5)/2 = -2/2 = -1
C)X²-8X+7=0
Δ = (-8)² - 4.1.7 = 64 - 28 = 36
x = [-(-8) +- √36]/2.1
x' = (8 + 6)/2 = 14/2 = 7
x" = (8 - 6)/2 = 2/2 = 1
D)X²-14X+ 48=0
Δ = (-14)² - 4.1.48 = 196 - 192 = 4
x = [-(-14) +- √4]/2.1
x' = (14 + 2)/2 = 16/2 = 8
x" = (14 - 2)/2 = 12/2 = 6
E)X²+5X+5=0
Δ = 5² - 4.1.5 = 25 - 20 = 5
x = [-5 +- √5]/2.1
x' = (-5 + √5)/2
x" = (-5 - √5)/2
G)X²+3X-28=O
Δ = 3² - 4.1.(-28) = 9 + 112 = 121
x = [-3 +- √121]/2.1
x' = (-3 + 11)/2 = 8/2 = 4
x" = (-3 - 11)/2 = -14/2 = -7
H)X²+3X-28=0
Δ = 3² - 4.1.(-28) = 9 + 112 = 121
Idem ao anterior.
I)-X²+X+12=0
Δ = 1² - 4.(-1).12 = 1 + 48 = 49
x = [-1 +- √49]/2.(-1)
x' = (-1 + 7)/(-2) = 6/(-2) = -3
x" = (-1 - 7)/(-2) = (-8)/(-2) = 4
J)-X²+X+12=0
Δ = 1² - 4.(-1).12 = 1 + 48 = 49
Idem ao anterior.
K)-X²+6X-5=0
Δ = 6² -4.(-1).(-5) = 36 -20 = 16
x = [-6 +- √16]/2.(-1)
x' = (-6 + 4)/(-2) = -2/(-2) = 1
x" = (-6 - 4)/(-2) = -10/(-2) = 5
L)6X²-X-5=0
Δ = (-1)² - 4.6.(-5) = 1 + 120 = 121
x = [-(-1) +- √121]/2.6
x' = [1 + 11]/12 = 12/12 = 1
x" =(1 - 11)/12 = -10/12 = -5/6
M)25X²-2X=-4
25x² - 2x + 4 = 0
Δ = (-2)² - 4.25.4 = 4 - 400 = -396
x = [-(-2) +- √-396]/2.25
x = [ 2 +- √-396]/50 --------- Solução no conjunto de Número Complexos
N) 2X=15-X²
x² + 2x - 15 = 0
Δ = 2² - 4.1.(-15) = 4 + 60 = 64
x = [-2 +- √64]/2.1
x' = (-2 + 8)/2 = 6/2 = 3
x" = (-2 - 8)/2 = -10/2 = -5
O)X²+3X-6=-8
x² + 3x - 6 + 8 = 0
x² + 3x + 2 = 0
Δ = 3² - 4.1.2 = 9 - 8 = 1
x = [-3 +- √1]/2.1
x' = (-3 + 1)/2 = -2/2 = -1
x" = (-3 -1)/2 = -4/2 = -2
P)(X+3)²=1
x² + 2x3 + 9 = 1
x² + 6x + 9 - 1 = 0
x² + 6x + 8 = 0
Δ = 6² - 4.1.8 = 36 - 32 = 4
x = [-6 +- √4]/2.1
x' = (-6 + 2)/2 = -4/2 = -2
x" = (-6 - 2)/2 = -8/2 = -4
Q)X(X+3)-40=0
x² + 3x - 40 = 0
Δ = 3² - 4.1.(-40) = 9 + 160 = 169
x = [-3 +- √169]/2.1
x' = (-3 + 13)/2 = 10/2 = 5
x" = (-3 - 13)/2 = -16/2 = -8
R)-X²+X+30=0
Δ = 1² - 4.(-1).30 = 121
x = [-1 +- √121]/2.(-1)
x' = [-1 + 11]/(-2) = 10/(-2) = -5
x" = [-1 - 11]/(-2) -12/(-2) = 6
S)(X-5)² = 1
x² + 2x5 + 25 - 1 = 0
x² + 10x + 24 = 0
Δ = 10² - 4.1.24 = 100 - 96 = 4
x = [-10 +- √4]/2.1
x' = -10 + 2/2 = -8/2 = -4
x" = -10 - 2/2 = -12/2 = -6
T)X²+3X-28=0
Δ = 3² - 4.1.(-28) = 9 + 112 = 121
x = [-3 +- √121]/2.1
x' = -3 + 11/2 = 8/2 = 4
x" = -3 - 11/2 = -14/2 = -7
Espero ter ajudado.
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