Question

Processo de Bhaskara/calcule a soma e o produto das raizes

Answer 1

2).

b). x² + x - 6 = 0

a = 1 | ♦ = b² - 4ac. | x1,2 = (-b ± √♦)/2a
b = 1 | ♦ = 1² - 4×1(-6). | x1,2 = (-1±5)/2×1
c = -6 | ♦ = 25 → √♦ = 5 | x1,2 = (-1±5)/2
_____________
x1 = (-1 + 5)/2
x1 = 4/2
x1 = 2
_______
x2 = (-1-5)/2
x2 = -6/2
x2 = -3
________

c). x² - 10x - 12 = 0

a = 1 ↓ | ♦ = (-10)² - 4×1(-12)
b = -10 ↓ | ♦ = 148
c = -12 ↓ | √♦ = 12,2
_______

x1,2 = [ -(-10) ± 12,2 ]/2×1

x1,2 = ( 10 ± 12,2 )/2

x1 = 11,1

x2 = -1,1
_________

d). 9x² + 5x + 1 = 4x²

9x² - 4x² + 5x + 1 = 0

5x² + 5x + 1 = 0

a = 5 ↓ | ♦ = b² - 4ac
b = 5 ↓ | ♦ = 5² - 4×5(1)
c = 1 ↓ | ♦ = 5 → √♦ = 2,2
________

x1,2 = ( -b ± √♦ )/2a

x1,2 = ( -5 ± 2,2 )/2×5

x1,2 = ( -5 ± 2,2 )/10

x1 = -0,28

x2 = -0,72
________________
3).

a) x² - 5x + 6 = 0

a = 1 ↓ | ♦ = b² - 4ac
b = -5 ↓ | ♦ = ( -5 )² - 4×1(6)
c = 6 ↓ | ♦ = 1 → √♦ = 1
__________

x1,2 = ( -b ± √♦ )/2a

x1,2 = [ -(-5) ± 1 ]/2×1

x1,2 = ( 5 ± 1 )/2

x1 = 6/2

x1 = 3
....
x2 = 4/2

x2 = 2
___________

b). 2x² - 10x - 12 = 0

a = 2 ↓ | ♦ = (-10)² - 4×2(-12)
b = -10 ↓ | ♦ = 196
c = -12 ↓ | √♦ = 14
_____________

x1,2 = [ -(-10) ± 14 ]/2×2

x1,2 = ( 10 ± 14 )/4

x1 = 24/4

x1 = 6
..
x2 = -4/4

x2 = -1
___________

c). 3x² - 21x + 9 = 0

a = 3 ↓ | ♦ = b² - 4ac
b = -21 ↓ | ♦ = (-21)² - 4×3(9)
c = 9 ↓ | ♦ = 333 → √♦ = 18,3
_________
x1,2 = ( -b ± √♦ )2a

x1,2 = [ -(-21) ± 18,3 ]/2×3

x1,2 = ( 21 ± 18,3 )/6

x1 = 6,55
...
x2 = ( 21 - 18,3 )/6

x2 = 0,45
__________

d). x² - 2x - 8 = 0

a = 1
b= -2
c = -8

.........

♦ = b² - 4ac

♦ = (-2)² - 4(-8)

♦ = 36 → √♦ = 6
...
x1,2 = ( -b ± √♦ )/2a

x1,2 = [ -(-2) ± 6 ]/2×1

x1,2 = ( 2 ± 6 )/2

x1 = 8/2

x1 = 4
...
x2 = -4/2

x2 = -2

Answer 2

2) respostas
b)( 2; -3 );
c)( 6; 4 )
d) ∆<0 não existe raiz real

a)
x^2 +x-6=0
∆=1^2-4•1•(-6)
∆=1+24
∆=25

x'= -1+√25/2
x'= -1+5/2
x'=4/2
x'=2

x"= -1-√25/2
x"= -1-5/2
x"= -6/2
x"= -3

c)
x^2-10x+24=0
∆=(-10)^2-4•1•24
∆=100-96
∆=4

x'= -(-10)+√4/2
x'= 10+2/2
x'=12/2
x'=6

x"= -(-10)-√4/2
x"=10-2/2
x"=8/2
x"= 4

d)
9x^2+3x+1=4x^2
9x^2-4x^2+3x+1=0
5x^2+3x+1=0

∆=3^2-4•5•(1)
∆=9-20
∆=-11
∆<0 não existe raiz real


3) soma e produtos das raízes se calcula através das fórmulas:
S= -b/a # P= c/a

a) x^2-5x+6=0

soma=-(-5)/1 = 5
produto=6/1= 6

B)2x^2-10x-12=0
soma= -(-10)/2=10/2=5
produto= -12/2= -6

C) 3x^2-21x+9=0
soma= -(-21)/3=21/3=7
produto=9/3=3

D) x^2-2x-8=0
soma= -(-2)/1= 2
produto= -8/1= -8