Question

1) Encontre os zeros das funções quadráticas a seguir:
a) F(x)= x2 -x – 6
b) F(x) = -x2 +3x +4
c) F(x) = 2x2 + 5x +2
d) F(x)= x2 + 6x -16
por favor preciso de ajuda :(

Answer 1

a) x² - x - 6 = 0

a = 1

b = - 1

c = - 6

∆ = b² - 4 . a . c

∆ = (-1)² - 4 . 1 . (-6)

∆ = 1 + 24

∆ = 25

x = - b ± √∆

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

2a

x' = -(-1) - 5

----------

2 . 1

x' = 1 - 5

------

2

x' = - 4

---

2

x' = - 2

x" = -(-1) + 5

-----------

2 . 1

x" = 1 + 5

-------

2

x" = 6

---

2

x" = 3

S = {-2 , 3}

b) - x² + 3x + 4 = 0

a = - 1

b = 3

c = 4

∆ = b² - 4 . a . c

∆ = 3² - 4 . (-1) . 4

∆ = 9 + 16

∆ = 25

x = - b ± √∆

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

2a

x' = - 3 - 5

---------

2 . (-1)

x' = - 8

-----

- 2

x' = 4

x" = - 3 + 5

---------

2 . (-1)

x" = 2

----

- 2

x" = - 1

S = {-1 , 4}

c) 2x² + 5x + 2 = 0

a = 2

b = 5

c = 2

∆ = b² - 4 . a . c

∆ = 5² - 4 . 2 . 2

∆ = 25 - 16

∆ = 9

x = - b ± √∆

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

2a

x' = - 5 - 3

---------

2 . 2

x' = - 8

---

4

x' = - 2

x" = - 5 + 3

---------

2 . 2

x" = - 2 (÷2)

---

4 (÷2)

x" = - 1

---

2

S = {- 2 , - 1/2}

d) x² + 6x - 16 = 0

a = 1

b = 6

c = - 16

∆ = b² - 4 . a . c

∆ = 6² - 4 . 1 . (-16)

∆ = 36 + 64

∆ = 100

x = - b ± √∆

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

2a

x' = - 6 - 10

-----------

2 . 1

x' = - 16

----

2

x' = - 8

x" = - 6 + 10

-----------

2 . 1

x" = 4

---

2

x" = 2

S = {-8 , 2}