Question

4. Resolva as seguintes equações de 2º grau:
a) 2x2 - 50 = 0
b) 5x2 - 15 = 0
c) 2x2 = 8x
d) 7x2 = - 14x
e) x2 + x - 7=5
f) 4x2 - x + 1 = x + 3x2
g) 3x2 + 5x = -x-9 + 2x2​

Answer 1

a) 2x² - 50 = 0

2x² = 0 + 50

2x² = 50

x² = 50

----

2

x² = 25

x = √25

x = ± 5

S = {-5 , +5}

b) 5x² - 15 = 0

5x² = 0 + 15

5x² = 15

x² = 15

---

5

x² = 3

x = √3

x = ± 1,73

S = {-1,73 , +1,73}

c) 2x² = 8x

2x² - 8x = 0

2x (x - 4) = 0

2x = 0

x = 0

---

2

x = 0

x - 4 = 0

x = 0 + 4

x = 4

S = {0 , 4}

d) 7x² = - 14x

7x² + 14x = 0

7x (x + 2) = 0

7x = 0

x = 0

---

7

x = 0

x + 2 = 0

x = 0 - 2

x = - 2

S = {0 , -2}

e) x² + x - 7 = 5

x² + x - 7 - 5

x² + x - 12 = 0

a = 1

b = 1

c = - 12

∆ = b² - 4 . a . c

∆ = 1² - 4 . 1 . (-12)

∆ = 1 + 48

∆ = 49

x = - b ± √∆

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

2a

x' = - 1 - 7

--------

2 . 1

x' = - 8

---

2

x' = - 4

x" = - 1 + 7

---------

2 . 1

x" = 6

---

2

x" = 3

S = {-4 , 3}

f) 4x² - x + 1 = x + 3x²

4x² - 3x² - x - x + 1

x² - 2x + 1 = 0

a = 1

b = - 2

c = 1

∆ = b² - 4 . a . c

∆ = (-2)² - 4 . 1 . 1

∆ = 4 - 4

∆ = 0

x = - b ± √∆

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

2a

x = - (-2) - 0

-----------

2 . 1

x = 2 - 0

-------

2

x = 2

---

2

x = 1

S = {1}

g) 3x² + 5x = - x - 9 + 2x²

3x² - 2x² + 5x + x + 9

x² + 6x + 9 = 0

a = 1

b = 6

c = 9

∆ = b² - 4 . a . c

∆ = 6² - 4 . 1 . 9

∆ = 36 - 36

∆ = 0

x = - b ± √∆

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

2a

x = - 6 - 0

---------

2 . 1

x = - 6

---

2

x = - 3

S = {-3}