Question

Resolva as equações
a) 2x²+x-3=0
b) -3x²+18x-15=0
c) 3x²+2x-1=0

Answer 1

a) 2x² + x - 3 = 0

a = 2

b = 1

c = - 3

Δ = b² - 4ac

Δ = 1² - 4.2.(- 3)

Δ = 1 + 24

Δ = 25

x = - b ± √Δ / 2a

x = - 1 ± √25 / 2.2

x = - 1 ± 5 / 4

x' = - 1 + 5 / 4

x' = 4 / 4

x' = 1

x'' = - 1 - 5 / 4

x'' = - 6 / 4 simplificando por 2

x'' = - 3/2

b) - 3x² + 18x - 15 = 0

a = - 3

b = 18

c = - 15

Δ = b² - 4ac

Δ = 18² - 4.(- 3).(- 15)

Δ = 324 - 180

Δ = 144

x = - b ± √Δ / 2a

x = - 18 ± √144 / 2.(- 3)

x = - 18 ± 12 / - 6

x' = - 18 + 12 / - 6

x' = - 6 / - 6

x' = 1

x'' = - 18 - 12 / - 6

x'' = - 30 / - 6

x'' = 5

b) 3x² + 2x - 1 = 0

a = 3

b = 2

c = - 1

Δ = b² - 4ac

Δ = 2² - 4.3.(- 1)

Δ = 4 + 12

Δ = 16

x = - b ± √Δ / 2a

x = - 2 ± √16 / 2.3

x = - 2 ± 4 / 6

x' = - 2 + 4 / 6

x' = 2 / 6 simplificando por 2

x' = 1/3

x'' = - 2 - 4 / 6

x'' = - 6 / 6

x'' = - 1