Question

Calcule as raizes das equacoes de 2 grau

1)
a) 5x²- 20 = 0

d) 7x²+ 5x = 0
e) 2x²+ 5x = 0
f) - x² + 4x = 0


2) quais das equacoes a seguir nao possuem raizes reais

a) - x² - 5 = 0
b) x² + 13 = 0
d) - x² + 2 =o
e) x² + 7 = 4

3) calcule as raizes de cada equacao

a) (2x + 3) ² - 9 = 12x
b) (3x - 1)² = 1
c) ( x - 2) . (x + 4) = 2 . (x + 4)

Answer 1

1
a =
5x² - 20 = 0
x² - 4 = 0
x² = 4
x = +-V4 = +-2 ***
d
7x² + 5x = 0
x( 7x + 5) = 0
x = 0
7x + 5 = 0
7x = -5
x = -5/7 ***
e
2x² + 5x = 0
x ( 2x + 5 ) = 0
x = 0
2x + 5 = 0
2x = -5
x = -5/2 ****
f
- x² + 4x = 0
x² - 4x = 0
x( x - 4) = 0
x = 0
x - 4 = 0
x = 4 ****
2
-x² - 5 = 0
x² + 5 = 0
x² = -5
x = +-V-5
não há raizes no campo real
b
x² + 13 = 0
x² = -13
x= +-V-13
idem acima
c
-x² + 2 = 0
x2 - 2 = 0
x² = 2
x = +-V2 ****
2raizes 
d
x² + 7 = 4
x² = 4 - 7
x² = -3
x = +-V-3
não há raizes no campo real ***

3
a
(2x + 3)² - 9 = 12x
[(2x)² + 2.2x.3 + 3² ] - 9 = 12x
4x² + 12x + 9 - 9 - 12x = 0
4x² = 0
x² = 0/4  = 0
x = 0 ****
b
( 3x - 1)²  = 1
(3x)² - 2.3x.1 + 1²  = 1
9x² - 6x + 1 - 1 = 0
9x² - 6x = 0
3x² - 2x = 0
x( 3x - 2) = 0
x = 0
3x - 2 = 0
3x = 2
x = 2/3 *****
c
( x - 2) ( x + 4 ) = 2 ( x + 4)
x² + 4x -2x - 8 = 2x + 8
x² + 2x - 8 - 2x - 8 = 0
x² -16 = 0
x² = 16
x = +-V16 = +-4 *****