resolve as equações completas no conjunto R:
a) x²+5x+4=0
b) 7x²+x+2=0
c)x²-18x+45=0
d)-x²-x+30=0
e)x²-6x+9=0
f) (x+3)²=1
Soluções para a tarefa
Explicação passo-a-passo:
x² + 5x + 4 = 0
a= 1; b = 5; c= 4
D = 5² - 4 . 1 . 4
D = 25 - 16
D = 9
x' = -5 + 3
2 .1
x' = -5 + 3
2
x' = -2
2
x' = -1
x" = -5 - 3
2 .1
x" = -5 - 3
2
x" = -8
2
x" = -4
7x² + x + 2 = 0
a= 7; b = 1; c= 2
D = 1² - 4 . 7 . 2
D = 1 - 56
D = -55
x² - 18x + 45 = 0
a= 1; b = -18; c= 45
D = -18² - 4 . 1 . 45
D = 324 - 180
D = 144
x' = -(-18) + 12
2 .1
x' = 18 + 12
2
x' = 30
2
x' = 15
x" = -(-18) - 12
2 .1
x" = 18 - 12
2
x" = 6
2
x" = 3
-x² - x + 30 = 0
a= -1; b = -1; c= 30
D = -1² - 4 . -1 . 30
D = 1 + 120
D = 121
x' = -(-1) + 11
2 .(-1)
x' = 1 + 11
-2
x' = 12
-2
x' = -6
x" = -(-1) - 11
2 .(-1)
x" = 1 - 11
-2
x" = -10
-2
x" = 5
x² - 6x + 9 = 0
a= 1; b = -6; c= 9
D = -6² - 4 . 1 . 9
D = 36 - 36
D = 0
x' = -(-6) + 0
2 .1
x' = 6 + 0
2
x' = 6
2
x' = 3
x" = -(-6) - 0
2 .1
x" = 6 - 0
2
x" = 6
2
x" = 3
x² + 6x + 9 - 1 = 0
x² + 6x + 8 = 0
a= 1; b = 6; c= 8
D = 6² - 4 . 1 . 8
D = 36 - 32
D = 4
x' = -6 + 2
2 .1
x' = -6 + 2
2
x' = -4
2
x' = -2
x" = -6 - 2
2 .1
x" = -6 - 2
2
x" = -8
2
x" = -4