Question

A) x ao quadrado -7x + 12 = 0

B) x ao quadrado -4x + 3 = 0

C) x ao quadrado - 6x + 5 = 0

D) 3x ao quadrado - 12x + 9 = 0

E) x ao quadrado + 2x - 35 = 0

F) x ao quadrado - 8x + 7 = 0

Answer 1

A) Δ = b2 - 4.a.c

Δ = -72 - 4 . 1 . 12

Δ = 49 - 4. 1 . 12

Δ = 1

Há 2 raízes reais.

x = (-b +- √Δ)/2a

x' = (--7 + √1)/2.1     x'' = (--7 - √1)/2.1

x' = 8 / 2     x'' = 6 / 2

x' = 4     x'' = 3

B) Δ = b2 - 4.a.c

Δ = -42 - 4 . 1 . 3

Δ = 16 - 4. 1 . 3

Δ = 4

x = (-b +- √Δ)/2a

x' = (--4 + √4)/2.1     x'' = (--4 - √4)/2.1

x' = 6 / 2     x'' = 2 / 2

x' = 3     x'' = 1

C) Δ = b2 - 4.a.c

Δ = -62 - 4 . 1 . 5

Δ = 36 - 4. 1 . 5

Δ = 16

x = (-b +- √Δ)/2a

x' = (--6 + √16)/2.1     x'' = (--6 - √16)/2.1

x' = 10 / 2     x'' = 2 / 2

x' = 5     x'' = 1

D) Δ = b2 - 4.a.c

Δ = -122 - 4 . 3 . 9

Δ = 144 - 4. 3 . 9

Δ = 36

x = (-b +- √Δ)/2a

x' = (--12 + √36)/2.3     x'' = (--12 - √36)/2.3

x' = 18 / 6     x'' = 6 / 6

x' = 3     x'' = 1

E) Δ = b2 - 4.a.c

Δ = 22 - 4 . 1 . -35

Δ = 4 - 4. 1 . -35

Δ = 144

x = (-b +- √Δ)/2a

x' = (-2 + √144)/2.1     x'' = (-2 - √144)/2.1

x' = 10 / 2     x'' = -14 / 2

x' = 5     x'' = -7

F) Δ = b2 - 4.a.c

Δ = -82 - 4 . 1 . 7

Δ = 64 - 4. 1 . 7

Δ = 36

x = (-b +- √Δ)/2a

x' = (--8 + √36)/2.1     x'' = (--8 - √36)/2.1

x' = 14 / 2     x'' = 2 / 2

x' = 7     x'' = 1