Question

Resolva as equações a seguir utilizando o Delta (∆): ² − 4. .

a)-x² +2x +3=0
b)x² +x-6=0
c) 5x² -3x -2=0
d)3x² +4x +1=0
e)-3x² +4x +4=0 ​

Answer 1

✔OLÁ!!!

A) - X² + 2X + 3 = 0

Δ = B² - 4 a.c

Δ = 2² - 4 . (- 1) . 3

Δ = 4 + 12

Δ = 16

X = - B ± √Δ /2.a

X = - 2 ± √16 /2.(-1)

X' = - 2 + 4 /-2

X' = 2/-2

X' = - 1

X" = - 2 - 4 /-2

X" = - 6/-2

X" = 3

B) X² + X - 6 = 0

Δ = B² - 4 a.c

Δ = 1² - 4 . 1 . (- 6)

Δ = 1 + 24

Δ = 25

X = - B ± √Δ /2.a

X = - 1 ± √25 /2.1

X' = - 1 + 5 /2

X' = 4/2

X' = 2

X" = - 1 - 5 /2

X" = - 6/2

X" = - 3

C) 5X² - 3X - 2 = 0

Δ = B² - 4 a.c

Δ = (- 3)² - 4 . 5 . (- 2)

Δ = 9 + 40

Δ = 49

X = - B ± √Δ /2.a

X = - (- 3) ± √49 /2.5

X' = 3 + 7 /10

X' = 10/10

X' = 1

X" = 3 - 7 /10

X" = - 4/10 ÷2

X" = - 2/5

D) 3X² + 4X + 1 = 0

Δ = B² - 4 a.c

Δ = 4² - 4 . 3 . 1

Δ = 16 - 12

Δ = 4

X = - B ± √Δ /2.a

X = - 4 ± √4 /2.3

X' = - 4 + 2 /6

X' = - 2/6 ÷2

X' = - 1/3

X" = - 4 - 2 /6

X" = - 6/6

X" = - 1

E) - 3X² + 4X + 4 = 0

Δ = B² - 4 a.c

Δ = 4² - 4 . (- 3) . 4

Δ = 16 + 48

Δ = 64

X = - B ± √Δ /2.a

X = - 4 ± √64 /2.(-3)

X' = - 4 + 8 /-6

X' = 4/-6 ÷2

X' = - 2/3

X" = - 4 - 8 /-6

X" = - 12/-6

X" = 2