Question

determine as raizes da equaçoes

2x²+x-1=0 b)2x²+2x-24=0

Answer 1

a)
2x² + x - 1 = 0
a = 2, b = 1; c = - 1

Δ = b² - 4ac
Δ = 1 - 4.2.(-1)
Δ = 1 + 8
Δ = 9
√Δ = 3

x = - b +/-√Δ
         2a

x' = - 1 + 3 = 2  (:2) =   1
         2.2       4  (:2)     2

x" = - 1 - 3 = - 4 = - 1
        2.2         4

Resp.: x = 1/2 e x = - 1

b)

2x² + 2x - 24 = 0 (:2)
x² + x - 12 = 0
a = 1; b = 1; c = - 12

Δ = b² - 4ac
Δ = 1 - 4.1.(-12)
Δ = 1 + 48
Δ = 49
√Δ = 7

x = - b +/- √Δ
         2a

x' = - 1 + 7 = 6/2 = 3
           2 

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

Resp.: x = 3 e x = - 4