Question

Determine as raizes de cada equação completa:

A) 4x² + 12x + 5 = 0
B) x² + 13x + 40 = 0
C) x² - 6x + 9 = 0

Answer 1

x² + 13 x + 40 = 0
Δ = b² - 4 .a . c
Δ = 13² - 4 . 1 . 40
Δ = 169 - 4 . 1 . 40
Δ = 169  - 160
Δ = 169 - 160
Δ = 9
\/¨¨9 = 3
x = - b +ou-3/2.1
x´= - 13 +ou- 3/2
x´= -13 + 3 / 2
x´= -10/2
x = - 5 
x" =-13 - 3/2
x" =-16/2
x" =- 8
x² - 6 x + 9 = 0
Δ = b² - 4 .a .c
Δ = -6² - 4 .1 . 9
Δ = 36 - 4 .1 . 9
Δ = 36 -36
Δ = 0
x = - b /2
x = -(-6)/2
x´=x" = 6/2⇒3
4 x² + 12 x + 5 = 0
Δ = b² - 4 . a . c
Δ=12² - 4 .4 . 5
Δ = 144 - 80
Δ = 64 \/¨¨64 = 8
x = - b +ou- 8/2.4
x = -12 +ou- 8/8
x´= -12 + 8/8
x´= -4/8
x´= -1/2
x" = -12 - 8 /8
x" = -20/8
x" = -5/2

Answer 2

x² + 13 x + 40 = 0Δ = b² - 4 .a . cΔ = 13² - 4 . 1 . 40Δ = 169 - 4 . 1 . 40Δ = 169  - 160Δ = 169 - 160Δ = 9\/¨¨9 = 3x = - b +ou-3/2.1x´= - 13 +ou- 3/2x´= -13 + 3 / 2x´= -10/2x = - 5 x" =-13 - 3/2x" =-16/2x" =- 8x² - 6 x + 9 = 0Δ = b² - 4 .a .cΔ = -6² - 4 .1 . 9Δ = 36 - 4 .1 . 9Δ = 36 -36Δ = 0x = - b /2x = -(-6)/2x´=x" = 6/2⇒34 x² + 12 x + 5 = 0Δ = b² - 4 . a . cΔ=12² - 4 .4 . 5Δ = 144 - 80Δ = 64 \/¨¨64 = 8x = - b +ou- 8/2.4x = -12 +ou- 8/8x´= -12 + 8/8x´= -4/8x´= -1/2x" = -12 - 8 /8x" = -20/8x" = -5/2