Question

determine as raízes das funções quadráticas abaixo(urgente pfvr)

a)f(x)=2x²+3x+1
b)f(x)=x²-4x+3
c)f(x)=2x²-4x+2
d)f(x)=2x²-50
e)f(x)=3x²+9x​

Answer 1

Resposta:

A) Δ =  $b^{2}$ - 4 · a · c

Δ = $3^{2}$ - 4 · 2 · 1

Δ = 9 · 8

Δ = 1

x = -b ± VΔ / 2 · a   (esse V representa a raiz)

x = -3 ± 1 / 2 · 2

x' = -3 + 1 / 4   =  -2/4

x'  = -0,5

x'' = -3 - 1 / 4

x'' = -4 / 4

x'' = -1

B) Δ =  $b^{2}$ - 4 · a · c

Δ = $1^{2}$ - 4 · (-4) · 3

Δ = 1 - (-48)

Δ = 49

x = -b ± VΔ / 2 · a  

x = -(-4) ± $\sqrt{49}$ / 2 · 1

x = 4 ± 7 / 2

x' = 4 + 7 / 2

x' = 5,5

x'' = 4 - 7 / 2

x'' = -1,5

C)Δ =  $b^{2}$ - 4 · a · c

Δ = -$4^{2}$ - 4 · 2 · 2

Δ = 16 - 16

Δ = 0

x = -b ± VΔ / 2 · a  

x = -(-4) ± $\sqrt{0}$ / 2 · 2

x = 4  ± 0 / 4

x' = 1

x'' = -1

D)∆ = $b^{2}$ – 4·a·c

∆ = $0^{2}$ – 4·2·(– 50)

∆ = – 8 · (– 50)

∆ = 400

x = -b ± VΔ / 2 · a  

x = 0 ± $\sqrt{400}$ / 2 · 2

x = ± 20 / 4

x' = 5

x'' = -5

E) ∆ = $b^{2}$ – 4·a·c

 ∆ = $9^{2}$ – 4 · 3 · 0

∆ = 81 - 0

∆ = 81

x = -b ± VΔ / 2 · a  

x = 9 ± $\sqrt{81}$ / 2 · 3

x = 9 ± 9 / 6

x' = 9 + 9 / 6

x' = 3

x'' = 9 - 9 / 6

x'' = 0

Espero ter ajudado : )