Question

² grau
A) 2x²+x-3=0
B) x²-5x-6=0
C) x²-7x+10=0
D) x²+5x+6=0

Answer 1

a) 2x² + x - 3 = 0

a = 2

b = 1

c = - 3

∆ = b² - 4 . a . c

∆ = 1² - 4 . 2 . (-3)

∆ = 1 + 24

∆ = 25

x = - b ± √∆

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

2a

x' = - 1 - 5

---------

2 . 2

x' = - 6 (÷2)

---

4 (÷2)

x' = - 3

---

2

x" = - 1 + 5

---------

2 . 2

x" = 4

---

4

x" = 1

S = {-3/2 , 1}

b) x² - 5x - 6 = 0

a = 1

b = - 5

c = - 6

∆ = b² - 4 . a . c

∆ = (-5)² - 4 . 1 . (-6)

∆ = 25 + 24

∆ = 49

x = - b ± √∆

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

2a

x' = - (-5) - 7

----------

2 . 1

x' = 5 - 7

-------

2

x' = - 2

---

2

x' = - 1

x" = - (-5) + 7

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

2 . 1

x" = 5 + 7

-------

2

x" = 12

---

2

x" = 6

S = {-1 , 6}

c) x² - 7x + 10 = 0

a = 1

b = - 7

c = 10

∆ = b² - 4 . a . c

∆ = (-7)² - 4 . 1 . 10

∆ = 49 - 40

∆ = 9

x = - b ± √∆

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

2a

x' = - (-7) - 3

-----------

2 . 1

x' = 7 - 3

-------

2

x' = 4

---

2

x' = 2

x" = - (-7) + 3

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

2 . 1

x" = 7 + 3

-------

2

x" = 10

---

2

x" = 5

S = {2 , 5}

d) x² + 5x + 6 = 0

a = 1

b = 5

c = 6

∆ = b² - 4 . a . c

∆ = 5² - 4 . 1 . 6

∆ = 25 - 24

∆ = 1

x = - b ± √∆

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

2a

x' = - 5 - 1

--------

2 . 1

x' = - 6

---

2

x' = - 3

x" = - 5 + 1

----------

2 . 1

x" = - 4

---

2

x" = - 2

S = {-3 , -2}