Question

Determine as as raízes das equações utilizando a fórmula resolutiva (fórmula de Bhaskara)
a)
$x {}^{2} - 4x - 5 = 0$
b)
$x {}^{2} + 12x + 36 = 0$
c)
$- t - 12 + t {}^{2} = 0$
d)
$3y { }^{2} + 1 - 4y = 0$
​

Answer 1

a) x² - 4x - 5 = 0

a = 1

b = - 4

c = - 5

∆ = b² - 4 . a . c

∆ = (-4)² - 4 . 1 . (-5)

∆ = 16 + 20

∆ = 36

x = - b ± √∆

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2a

x' = - (-4) - 6

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

2 . 1

x' = 4 - 6

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2

x' = - 2

---

2

x' = - 1

x" = - (-4) + 6

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

2 . 1

x" = 4 + 6

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2

x" = 10

---

2

x" = 5

S = {-1 , 5}

b) x² + 12x + 36 = 0

a = 1

b = 12

c = 36

∆ = b² - 4 . a . c

∆ = 12² - 4 . 1 . 36

∆ = 144 - 144

∆ = 0

x = - b ± √∆

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

2a

x = - 12 - 0

----------

2 . 1

x = - 12

---

2

x = - 6

S = {-6}

c) - t - 12 + t² = 0

a = 1

b = - 1

c = - 12

∆ = b² - 4 . a . c

∆ = (-1)² - 4 . 1 . (-12)

∆ = 1 + 48

∆ = 49

t = - b ± √∆

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

2a

t' = - (-1) - 7

----------

2 . 1

t' = 1 - 7

-----

2

t' = - 6

----

2

t' = - 3

t" = - (-1) + 7

-----------

2 . 1

t" = 1 + 7

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2

t" = 8

---

2

t" = 4

S = {-3 , 4}

d) 3y² + 1 - 4y = 0

a = 3

b = - 4

c = 1

∆ = b² - 4 . a . c

∆ = (-4)² - 4 . 3 . 1

∆ = 16 - 12

∆ = 4

y = - b ± √∆

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

2a

y' = - (-4) - 2

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

2 . 3

y' = 4 - 2

-------

6

y' = 2 (÷2)

---

6 (÷2)

y' = 1

---

3

y" = - (-4) + 2

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

2 . 3

y" = 4 + 2

-------

6

y" = 6

----

6

y" = 1

S = {(1/3 , 1)}