Question

de as raizes das funcoes
a) 3x^2 -7x+ 4=0
b) x^2 -x-20=0
c) -5x -75=0​

Answer 1

a) 3x^2 - 7x + 4 = 0

a = 3

b = -7

c = 4

Δ = b^2 - 4 . a . c

Δ = (-7)^2 - 4 . 3 . 4

Δ = 49 - 12 . 4

Δ = 49 - 48

Δ = 1

x = -b ± √Δ /2 . a

x = -(-7) ± √1 /2 . 3

x = 7 ± 1 /6

x' = 7 + 1 /6

x' = 8/6

x' = 4/3

x" = 7 - 1 /6

x" = 6/6

x" = 1

S = {4/3 , 1}

b) x^2 - x - 20 = 0

a = 1

b = -1

c = -20

Δ = b^2 - 4 . a . c

Δ = (-1)^2 - 4 . 1 . (-20)

Δ = 1 - 4 . (-20)

Δ = 1 - (-80)

Δ = 1 + 80

Δ = 81

x = -b ± √Δ /2 . a

x = -(-1) ± √81 /2 . 1

x = 1 ± 9 /2

x' = 1 + 9/2

x' = 10/2

x' = 5

x" = 1 - 9 /2

x" = -8/2

x" = -4

S = {5 , -4}

c) -5x - 75 = 0

-5x = 0 + 75

-5x = 75

x = 75/-5

x = -15