Question

Resolva as seguintes Equações:
1- X² - 5x+6=0
a) X1 = 3 e X11 = 2
b) X' = 2 e X"= 1
c) X1 = 4 e X11 = 0
d) X = 1 e X11 = 1
2- X² + 5X-6=0
a) X1 = 4 e X11 = 2
b) X1 = 5 e X11 = 2
c) X1 = 2 e X11 = 2
d) X' = 6 e X11 = -1
3- X2 + 8x + 12 = 0
a)
b)
c)
d)
X'= 1 e X11 = 9
X'= -2 e X11 = -6
X1 = 3 e X11 = -7
X'= 3 e X11 = -9
4- 2x2 + 7x + 3 =0
a) x1 = 7 e X11 = 9
b) Xi = 1 e X" = 5
c) X1 = - 1/2 e = -6
d) X1 = 3 e X11 = 2
5- 3X2 - 2x-1=0
a) Xi = 1 e X11 = -1/3
b) Xi = 1 e X11 = -1/4
c) X'= 1 e X11 = -1/5
d) X = 1 e X11 = -1/6​

Answer 1

1)x² - 5x + 6=0

A= 1

B= - 5

C=6

∆= b²- 4ac

∆=( - 5)² - 4 • 1 • 6

∆= 25 - 24

∆= 1

x= - b ± √∆ /2a

x= - ( - 5) ± √1 / 2 • 1

x= 5 ± 1/2

x'= 5 + 1/2 = 6/2 = 3

x''= 5- 1/2 = 4/2 = 2

S= ( 3 , 2)

2) x² + 5x - 6 = 0

∆= 5² - 4 • 1 • ( - 6)

∆= 25 + 24

∆= 49

x= - 5 ± √49 / 2 • 1

x= - 5 ± 7 / 2

x'= - 5 + 7/2 = 2/2 = 1

x''= - 5 - 7/2 = - 12/2 = - 6

S= ( - 6 , 1)

3) x² + 8x + 12 = 0

∆= 8² - 4 • 1 • 12

∆= 64 - 48

∆= 16

x= - 8 ± √16 /2 • 1

x= - 8 ± 4/2

x'= - 8 + 4/2 = - 4/2 = - 2

x''= - 8 - 4/2 = - 12/2 = - 6

S= ( - 2 , - 6)

4) 2x² + 7x + 3 = 0

∆= 7² - 4 • 2 • 3

∆= 49 - 24

∆= 25

x= - 7 ± √25/2 • 2

x= - 7 ± 5/4

x'= - 7 + 5/4 = - 2/4 = -1/2

x''= - 7 - 5/4 = - 12/4 = - 3

S= ( - 1/2 , - 3)

5) 3x²- 2x - 1 = 0

∆= ( - 2)² - 4 • 3 • ( - 1)

∆= 4 + 12

∆= 16

x= - ( - 2) ± √16 / 2 • 3

x= 2 ± 4/6

x'= 2 + 4/6 = 6/6 = 1

x''= 2 - 4/6 = - 2/6 = - 1/3

S= ( 1 , -1/3)