Question

equação de 2 grau; a)x2+3x-10=0 b)6x2+x-1=0 c)2x2-4x+3=0 d)x2-6x+9=0 e)-x2+x+12=0

Answer 1

Resposta:

a) x' = 2

x" = - 5

b) x' = 1/3

x" = - 1/2

c) x' = 3/2

x" = 1/2

d) x' = x" = 3

e) x' = - 3

x" = 4

Explicação passo-a-passo:

a) x² + 3x - 10 = 0

a = 1, b = 3, c = - 10

Δ = b² - 4ac

Δ = (3)² - 4. 1. - 10

Δ = 9 + 40

Δ = 49

x = - b ± √Δ / 2a

x = - (3) ± √49 / 2.1

x = - 3 ± 7 / 2

x' = - 3 + 7 / 2 = 4 / 2 = 2

x" = - 3 - 7 / 2 = - 10 / 2 = - 5

b) 6x² + x - 1 = 0

a = 6, b = 1, c = - 1

Δ = b² - 4ac

Δ = (1)² - 4. 6. - 1

Δ = 1 + 24

Δ = 25

x = - b ± √Δ / 2a

x = - (1) ± √25 / 2.6

x = - 1 ± 5 / 12

x' = - 1 + 5 / 12 = 4/12 = 1/3

x" = - 1 - 5 / 12 = - 6/12 = - 1/2

c) 2x² - 4x + 3 = 0

a = 2, b = - 4, c = 3

Δ = b² - 4ac

Δ = (- 4)² - 4. 1. 3

Δ = 16 - 12

Δ = 4

x = - b ± √Δ / 2a

x = - (- 4) ± √4 / 2.2

x = 4 ± 2 / 4

x' = 4 + 2 / 4 = 6/4 = 3/2

x" = 4 - 2 / 4 = 2/4 = 1/2

d) x² - 6x + 9 = 0

a = 1, b = - 6, c = 9

Δ = b² - 4ac

Δ = (- 6)² - 4. 1. 9

Δ = 36 - 36

Δ = 0

x = - b ± √Δ / 2a

x = - (- 6) ± √0 / 2.1

x = 6 ± 0 / 2

x' = 6 + 0 / 2 = 6/2 = 3

x" = 6 - 0 / 2 = 6/2 = 3

e) - x² + x + 12 = 0

a = - 1, b = 1, c = 12

Δ = b² - 4ac

Δ = (1)² - 4. - 1. 12

Δ = 1 + 48

Δ = 49

x = - b ± √Δ / 2a

x = - (1) ± √49 / 2. - 1

x = - 1 ± 7 / - 2

x' = - 1 + 7 / - 2 = 6/ - 2 = - 3

x" = - 1 - 7 / - 2 = - 8/ - 2 = 4

Espero ter ajudado!!