Question

a) 3x² – 7x + 4 = 0

b) 9y² – 12y + 4 = 0



c) 5x² + 3x + 5 = 0

Answer 1

a) 3x² – 7x + 4 = 0         a = 3      b = -7      c = 4

Δ = b² - 4ac

Δ = -7² - 4.3.4

Δ = 49 - 48

Δ = 1

x = -b +- √Δ/2a

x = -(-7) +- √1/2.3

x = 7 +- 1/6

x' = 7+ 1/6 = 8/6    (:2)

x' = 4/3

x" = 7 - 1/6 = 6/6

x" = 1

b) 9y² – 12y + 4 = 0         a = 9      b = -12      c = 4

Δ = b² - 4ac

Δ = -12² - 4.9.4

Δ = 144 - 144

Δ = 0

x = -b +- √Δ/2a

x = -(-12) +- √0/2.9

x = 12 +- 0/18

x' = 12 + 0/18 = 12/18    (:6)

x' = 2/3

x" = 12 - 0/18 = 12/18      (:6)

x" = 2/3

 c) 5x² + 3x + 5 = 0          a = 5      b = 3      c = 5

Δ = b² - 4ac

Δ = 3² - 4.5.5

Δ = 9 - 100

Δ = - 91

x = -b +- √Δ/2a

x = - 3 +- √-91/2.5

x = - 3 +- √-91/10    Não existem raízes em |R quando Δ < 0