Question

Resolva a equação de segundo grau completa, utilizando a Fórmula de Bhaskara: a) 2 x2 + 7x + 5 = 0 R=-9
b) X2 + 5x + 6 = 0
c) X2 – 5x + 6 = 0
d) X2 + 6x + 5 = 0
e) X2 – 8x + 15 = 0
f) X2 – 23x +120 = 0
g) X2 +x – 12 = 0 h) 4x2 – 20x – 9 = 0
i) 15x2- 3x – 2 = 0 j) X2 -2x – 8 = 0

Answer 1

Resposta:

a) 2x2 + 7x + 5 = 0

a=2

b= 7

c= 5

Delta :

7^2 -4.2.5

49-4.10

49-40

9

Raiz de 9 = 3

X= 7+-3/2.2

X1= 7+3/4 = 10/4= 5/2 ou 2,5

X2 = 7-3/4 = 4/4 = 1

b) X2 + 5x + 6 = 0

a= 1

b=5

c=6

Delta :

5^2 -4.1.6

25-4.6

25-24

1

Raiz de 1= 1

X=5+-1/2.1

X1=5+1/1 = 6/1= 6

X2 =5-1/1= 4/1 = 4

c) X2 – 5x + 6 = 0

a= 1

b=(-5)

c=6

Delta :

-5^2 -4.1.6

25-4.6

25-24

Raiz de 1 =1

X=-5+1/2.1

X1=-5+1/1= -4/1 =-4

X2 =-5-1/1= -6/1=-6

d) X2 + 6x + 5 = 0

a= 1

b=6

c=5

Delta :

6^2 -4.1.5

36-4.5

49-20

29

Raiz de 29 = 5,3

X=6+-5,3/2.1

X1=6+5,3/1= 11,3

X2 =6-5,3/1=0,7

e) X2 – 8x + 15 = 0

a= 1

b=(-8)

c=15

Delta :

-8^2 -4.1.15

64-4.15

64-60

4

Raiz de 4= 2

X=-8+-2/2.1

X1=-8+2/1=-6

X2 =-8-2/1= -10

f) X2 – 23x +120 = 0

a= 1

b=(-23)

c=120

Delta :

-23^2 -4.1.120

529-4.120

529-480

49

Raiz de 49 =7

X=-23+-7/2.1

X1=-23+7/1=-16

X2 =-23-7/1= -30

g) X2 +x – 12 = 0

a= 1

b=1

c=(-12)

Delta :

1^2 -4.1.(-12)

1-4.(-12)

1+48

Raiz de 49 = 7

X=1+-7/2.1

X1=1+7/1=8

X2 =1-7/1= -6

h) 4x2 – 20x – 9 = 0

a= 4

b=(-20)

c=(-9)

Delta :

-20^2 -4.4.(-9)

400-4.(-36)

400+ 144

544

Raiz de 544 = 23,3

X=-20+-23,3/2.4

X1=-20+23,3/2.4 = 43,3/8=5,4

X2 =-20-23,3/2.4 = -3,3/8= -0,4

i) 15x2- 3x – 2 = 0

a= 15

b=(-3)

c=(-2)

Delta :

-3^2 -4.15.(-2)

9-4.(-30)

9+ 120

129

Raiz de 129= 10,9

X=-3+-10,9/2.15

X1=-3+10,9/2.15= 7,9/30 = 0,2

X2 =-3-10,9/2.15 = -13,9/30=-0,4

j) X2 -2x – 8 = 0

a= 1

b=(-2)

c=(-8)

Delta :

-2^2 -4.1.(-8)

4-4.(-8)

4+32

36

Raiz de 36= 6

X=-2+-6/2.1

X1=-2+6/1=4

X2 =-2-6/1= -8

Espero ter ajudado