Por meio da fórmula de Bhaskara, determine as raízes de cada equação:
a) x² - 6x + 5 = 0
b) 3x² + 4x + 1 = 0
c) x² - 8x + 16 = 0
d) x² - 13x + 22 = 0
e) -x² + 10x - 25 = 0
f) 7x² - 1x - 1 = 0
g) x² - 11x + 10 = 0
h) -x² + 5x - 8 = 0
Respostas
Explicação passo-a-passo:
x² - 6x + 5 = 0
a= 1; b = -6; c = 5
D = -6² - 4 . 1 . 5
D = 36 - 20
D = 16
x' = -(-6) + 4
2 .1
x' = 6 + 4
2
x' = 10
2
x' = 5
x" = -(-6) - 4
2 .1
x" = 6 - 4
2
x'' = 2
2
x'' = 1
3x² + 4x + 1 = 0
a= 3; b = 4; c = 1
D = 4² - 4 . 3 . 1
D = 16 - 12
D = 4
x' = -4 + 2
2 .3
x' = -4 + 2
6
x' = -2
6
x' = -1/3
x" = -4 - 2
2 .3
x" = -4 - 2
6
x'' = -6
6
x'' = -1
x² - 8x + 16 = 0
a= 1; b = -8; c = 16
D = -8² - 4 . 1 . 16
D = 64 - 64
D = 0
x' = -(-8) + 0
2 .1
x' = 8 + 0
2
x' = 8
2
x' = 4
x" = -(-8) - 0
2 .1
x" = 8 - 0
2
x'' = 8
2
x'' = 4
x² - 13x + 22 = 0
a= 1; b = -13; c = 22
D = -13² - 4 . 1 . 22
D = 169 - 88
D = 81
x' = -(-13) + 9
2 .1
x' = 13 + 9
2
x' = 22
2
x' = 11
x" = -(-13) - 9
2 .1
x" = 13 - 9
2
x'' = 4
2
x'' = 2
-x² + 10x - 25 = 0
a= -1; b = 10; c = -25
D = 10² - 4 . -1 . (-25)
D = 100 - 100
D = 0
x' = -10 + 0
2 .(-1)
x' = -10 + 0
-2
x' = -10
-2
x' = 5
x" = -10 - 0
2 .(-1)
x" = -10 - 0
-2
x'' = -10
-2
x'' = 5
7x² - -x - 1 = 0
a= 7; b = -1; c = -1
D = -1² - 4 . 7 . (-1)
D = 1 + 28
D = 29
x' = -(-1) + V29
2 .7
x' = 1 + V29
14
x" = -(-1) - V29
2 .7
x" = 1 - V29
14
x² - 11x + 10 = 0
a= 1; b = -11; c = 10
D = -11² - 4 . 1 . 10
D = 121 - 40
D = 81
x' = -(-11) + 9
2 .1
x' = 11 + 9
2
x' = 20
2
x' = 10
x" = -(-11) - 9
2 .1
x" = 11 - 9
2
x'' = 2
2
x'' = 1
-x² + 5x - 8 = 0
a= -1; b = 5; c = -8
D = 5² - 4 . -1 . (-8)
D = 25 - 32
D = -7