Question

x²+8x12=0

x²=12x+36=0

3x²-7x+2=0

x²+3x-1=0

2x-²20x+50=0

12x²-7x+1=0

x²-4x-21=0

x²+2+2=0

x²-3x+1=0

2x²-4x+3=0

2x²-20x+50=0

-2x²+x+3=0

Answer 1

a) x² + 8x +12 = 0
▲ = b² - 4a*c
▲ = 16 
 x =(-b ±√▲)/2a
x = ( -8 ±4)/2 ⇒ x1 = -2  ; x2 = -6

b) x² +12x+36=0
▲ = 0
x = (-12±0)/2 = -6 ⇒ x1=x2= -6

c) 3x²-7x+2=0
▲ = 25
x = (7 ± 5)/2*3 ⇔ x = (7 ± 5)/6  ⇔ x1 = 2 ; x2 =1/3

d) x²+3x-1=0
▲ = 13
x = (-3±√13)/2 ⇔ x1 = 1/2(-3 -√13) ; x2 = 1/2(-3 + √13)

e) 2x²-20x+50=0 
▲= 0
x = (20 ± 0)/2*2 = 20/4 = 5 ⇔ x1=x2=5

f) 12x²-7x+1=0
▲= 1
x = (7 ± √1)/2*12 ⇔ x1 = 8/24 = 1/3  ;  x2 = 6/24 = 1/4

g) x²-4x-21=0
▲=100
x = (4 ± √100)/2 ⇔ x1 = 14/2 = 7 ; x2 = -6/2 = -3

h) x²+2+2=0
▲= -4 → √▲ = √ 4i² ⇔ √▲ = ±2i (raízes complexas)
x1 = (-2 +2i) /2*1 ⇔ x1 = -1 + i
x2 = (-2 -2i) /2*1 ⇔ x2 = -1 - i

i) x²-3x+1=0
▲ = 5
x = (3±√5)/2*1 ⇔ x1 = (3 + √5)/2  ; x2 = (3 - √5)/2

j) 2x²-4x+3=0
▲= -8 ⇒ √▲ = √8i² ⇔ √▲ = ±2i√2
x = (4 ± 2i√2)/2*2
x1 = (4 + 2i√2)/4 ⇔ x1 = (2 + i√2)/2
x2 = (4 - 2i√2)/4 ⇔ x1 = (2 - i√2)/2

h) 2x²-20x+50=0
▲= 0
x = (20 ± 0)/2*2 = 20/4 = 5 ⇔ x1=x2=5

m) -2x²+x+3=0 
▲=25
x= (-1±√25)/2*(-2) ⇔ x= (-1 ± 5)/-4
x1= 4/-4 = -1
x2= -6/-4 = 3/2

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Obrigado pela oportunidade 
Boa sorte, bons estudos!
SSRC - 2015 
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