Question

Resolva as equações do 2º grau usando fatoração:
a) x² - 2x - 35 = 0
b) y² - 6y + 9 = 0
c) x² + 2x - 15 = 0
d) y² + 5y + 6 = 0
e) y² + 2y + 1 = 0
f) x² - 9x - 36 = 0
g) x² - 14x + 49 = 0

Answer 1

a) x² - 2x - 35 = 0
x=-(2)+-√(-2)²-4.1.(-35)/2.1
x=2+-√2²+4.35/2
x=2+-√4+140/2
x=2+-√144/2
x=2+-√12²/2
x=2+-12/2
x'=2+12/2 x'=7
x"=2-12/2 x"=-5

b) y² - 6y + 9 = 0
(y-3)²=0
y² -2y×3+3² =0
y² -6y+9=0
(y-3)² =0
y-3=0
y-3+3=0+3
y=3

c) x² + 2x - 15 = 0
x=-2+-√2²-4.1.(-15)/2.1
x=-2+-√4+4.15/2
x=-2+-√4+60/2
x=-2+-√64/2
x-2+-√8² /2
x=-2+-8/2
x'=-2+8/2 x'=3
x"=-2-8/2 x"=-5

d) y² + 5y + 6 = 0
y=-5+-√5²-4.1.6/2.1
y=-5+-√25-(4.6)/2
y=-5+-√25-24/2
y=-5+-√1/2
y=-5+-1/2
y'=-5+1/2 y'=-2
y"=-5-1/2 y"=-3

e) y² + 2y + 1 = 0
(y+1)² =0
y² +2y×1+1=0
y² +2y+1=0
(y+1)² =0
y+1=0
y+1-1=0-1
y=1

f) x² - 9x - 36 = 0
x=-(-9)+-√(-9)²-4.1.(-36)/2.1
x=9+-√9² +4.36/2
x=9+-√81+144/2
x=9+-√225/2
x=9+-√15² /2
x=9+-15/2
x'=9+15/2 x'=12
x"=9-15/2 x"=-3

g) x² - 14x + 49 = 0
(×-7)²=0
x² -2×.7+7² =0
x² 14×+49=0
(×-7)² =0
×-7=0
x-7+7=0+7
x=7