Question

1) Determine as raízes das equações utilizando a fórmula resolutiva.a) 2x²+x-1=0b) 2x²+2x-24=0c) 3x²-4x-2=-3d) 1/4x²+5x/4-6=0e) x²+5x-2=-8

Answer 1

a)2 x² + x - 1 = 0
Δ = b² - 4,a,c
Δ = 1² - 4 . 2 . - 1
Δ = 1 + 8
 Δ = 9 ⇒√ 9 = 3
x = - b + ou - 3 / 2.2
x´= -1 + 3 /4
x´= 2/4 = 1/2
x´´ = -1 - 3 / 4
x´´ = -4/4 = - 1
S = {-1 ; 1/2 }
b)2 x² + 2 x - 24 = 0
Δ = b² - 4.a.c
Δ = 2² - 4. 2 . -24
Δ = 4 + 192
Δ = 196 ⇒ √ 196 = 14
x = - b + ou - 14 / 2 .2
x´= -2 + 14 / 4
x´= 12/4 = 3
x´´ = -2 - 14 / 4
x´´ = -16/4 = - 4
S = {3 ; -4 }

c)3 x² - 4 x - 2 = - 3
3 x² - 4 x - 2 + 3 = 0
3 x² - 4 x + 1 = 0
Δ = b² - 4 .a.c
Δ = (-4)² - 4 . 3 . 1 
Δ = 16  - 12
Δ = 4 ⇒ √ 4 = 2
x = - b + ou - 2 / 2.3
x´= -(-4) + 2 / 6
x´= 4 + 2 / 6 = 6/6 = 1
x´´ = 4 - 2 / 6 = 2/6 = 1/3
S = 1 ; 1/3 }
d)1/4 x² + 5/4) x - 6 = 0
a = 1/4
b = 5/4 
c = - 6
Δ = b² - 4.a.c
Δ = (5/4)² - 4 . 1/4 . -6/1
Δ = 25/16 + 24/4
Δ = 25/16 + 6
Δ = 25/16+96/16
Δ = 121/16 ⇒√ 121/16 = 11/4
x = - b + ou - 11/4 / 2. 1/4
x = -5/4 + 11/4 / 2/4
x = 5/4 + 11/4  /  1/2
x = 5/4 + 11/4 x 2/1
x = 5/4 + 22/4
x = 27/4
x´´ = 5/4 - 22/4
x´´ = -17/4
S = -17/4 ; 27/4 }

e)x² + 5 x - 2 = - 8
x² + 5 x - 2 + 8 = 0
x² + 5 x + 6 = 0
Δ = b² - 4.a.c
Δ = 5² - 4.1 . 6
Δ = 25 - 24
Δ = 1 ⇒ √1 = 1
x = - b + ou - 1/2
x = -5 + 1 / 2
x´= -4/2 = - 2
x´´ = -5 - 1 /2 = -6 / 2 = - 3
S = {-2 ; - 3 }