Question

Resolva as equações e coloque em bhaskara x= -b+- √/\:
A)6x2-x-1=0

B)9x2+2x+1=0

C)3x2-7x+2=0

D)25x2-10x+1=0

Answer 1

A) 6x² - x - 1 = 0

a = 6

b = - 1

c = - 1

∆ = b² - 4 . a . c

∆ = (-1)² - 4 . 6 . (-1)

∆ = 1 + 24

∆ = 25

x = - b ± √∆

------------

2a

x' = - (-1) - 5

------------

2 . 6

x' = 1 - 5

-------

12

x' = - 4 (÷4)

----

12 (÷4)

x' = - 1

---

3

x" = - (-1) + 5

-----------

2 . 6

x" = 1 + 5

-------

12

x" = 6 (÷6)

----

12 (÷6)

x" = 1

---

2

S = {-1/3 , 1/2}

B) 9x² + 2x + 1 = 0

a = 9

b = 2

c = 1

∆ = b² - 4 . a . c

∆ = 2² - 4 . 9 . 1

∆ = 4 - 36

∆ = - 32

delta negativo não há raízes reais

S = { }

c) 3x² - 7x + 2 = 0

a = 3

b = - 7

c = 2

∆ = b² - 4 . a . c

∆ = (-7)² - 4 . 3 . 2

∆ = 49 - 24

∆ = 25

x = - b ± √∆

------------

2a

x' = - (-7) - 5

-----------

2 . 3

x' = 7 - 5

-------

6

x' = 2 (÷2)

---

6 (÷2)

x' = 1

---

3

x" = - (-7) + 5

------------

2 . 3

x" = 7 + 5

-------

6

x" = 12

----

6

x" = 2

S = {1/3 , 2}

d) 25x² - 10x + 1 = 0

a = 25

b = - 10

c = 1

∆ = b² - 4 . a . c

∆ = (-10)² - 4 . 25 . 1

∆ = 100 - 100

∆ = 0

x = - b ± √∆

------------

2a

x = - (-10) - 0

-------------

2 . 25

x = 10 - 0

--------

50

x = 10 (÷10)

-----

50 (÷10)

x = 1

---

5

S = {1/5}