Atividade: Introdução a Completar Quadrado

Nesta atividade, nós vamos praticar a completar quadrado para expressões em que o coeficiente do termo principal é um ou outro valor.

Q1:

Sendo π‘₯ βˆ’ 1 0 π‘₯ = ( π‘₯ + 𝑝 ) + π‘ž 2 2 , qual Γ© o valor de 𝑝 e de π‘ž ?

  • A 𝑝 = 5 , π‘ž = βˆ’ 2 5
  • B 𝑝 = βˆ’ 5 , π‘ž = 2 5
  • C 𝑝 = βˆ’ 1 0 , π‘ž = βˆ’ 1 0 0
  • D 𝑝 = βˆ’ 5 , π‘ž = βˆ’ 2 5
  • E 𝑝 = 1 0 , π‘ž = βˆ’ 1 0 0

Q2:

Dado βˆ’ π‘₯ + 3 π‘₯ + 4 = π‘Ž ( π‘₯ + 𝑝 ) + π‘ž 2 2 , qual o valor de π‘Ž , 𝑝 e π‘ž ?

  • A π‘Ž = 1 , 𝑝 = 3 2 , π‘ž = 9 4
  • B π‘Ž = βˆ’ 1 , 𝑝 = 3 2 , π‘ž = 9 4
  • C π‘Ž = βˆ’ 1 , 𝑝 = 3 , π‘ž = 4
  • D π‘Ž = βˆ’ 1 , 𝑝 = βˆ’ 3 2 , π‘ž = 2 5 4
  • E π‘Ž = 1 , 𝑝 = βˆ’ 3 , π‘ž = βˆ’ 4

Q3:

Escreva a equação π‘₯ = 3 0 βˆ’ 1 3 π‘₯ 2 na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž 2 .

  • A ο€Ό π‘₯ + 1 3 2  = 3 0 2
  • B ο€Ό π‘₯ βˆ’ 1 3 2  = 2 8 9 4 2
  • C ο€Ό π‘₯ + 1 6 9 4  = 2 8 9 4 2
  • D ο€Ό π‘₯ + 1 3 2  = 2 8 9 4 2
  • E ο€Ό π‘₯ + 1 6 9 4  = 3 0 2

Q4:

Escreva a equação 3 π‘₯ + 𝑏 π‘₯ + 𝑐 = 0  na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž  .

  • A ο€½ π‘₯ βˆ’ 𝑏 6  = 𝑏 βˆ’ 1 2 𝑐 3 6  
  • B ο€½ π‘₯ + 𝑏 3  = 𝑏 βˆ’ 3 𝑐 9  
  • C ο€½ π‘₯ + 𝑏 6  = βˆ’ 𝑐 3 
  • D ο€½ π‘₯ + 𝑏 6  = 𝑏 βˆ’ 1 2 𝑐 3 6  
  • E ο€½ π‘₯ βˆ’ 𝑏 3  = 𝑏 βˆ’ 3 𝑐 9  

Q5:

Escreva a equação π‘₯ + 6 π‘₯ βˆ’ 3 = 0 2 por completamento do quadrado.

  • A ( π‘₯ + 3 ) βˆ’ 9 = 0 2
  • B ( π‘₯ βˆ’ 3 ) βˆ’ 1 2 = 0 2
  • C ( π‘₯ βˆ’ 3 ) βˆ’ 9 = 0 2
  • D ( π‘₯ + 3 ) βˆ’ 1 2 = 0 2
  • E ( π‘₯ + 6 ) βˆ’ 3 9 = 0 2

Q6:

Escreva a equação 1 + π‘₯ = π‘₯ 2 na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž 2 .

  • A ο€Ό π‘₯ + 1 2  = 5 4 2
  • B ο€Ό π‘₯ βˆ’ 1 4  = 5 4 2
  • C ο€Ό π‘₯ βˆ’ 1 2  = 1 2
  • D ο€Ό π‘₯ βˆ’ 1 2  = 5 4 2
  • E ο€Ό π‘₯ βˆ’ 1 4  = 1 2

Q7:

Escreva a equação π‘₯ + π‘₯ + 1 = 0  na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž  .

  • A ο€Ό π‘₯ + 1 2  = βˆ’ 1 
  • B ο€Ό π‘₯ + 1 4  = βˆ’ 3 4 
  • C ο€Ό π‘₯ βˆ’ 1 2  = βˆ’ 3 4 
  • D ο€Ό π‘₯ + 1 2  = βˆ’ 3 4 
  • E ο€Ό π‘₯ + 1 4  = βˆ’ 1 

Q8:

Escreva a equação 3 π‘₯ βˆ’ 1 = 0 2 na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž 2 .

  • A ο€Ό π‘₯ βˆ’ 1 3  = 1 9 2
  • B ο€Ό π‘₯ βˆ’ 1 3  = 0 2
  • C π‘₯ = 1 9 2
  • D π‘₯ = 1 3 2

Q9:

Escreva a equação π‘₯ βˆ’ π‘₯ = 3 4 2 na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž 2 .

  • A ο€Ό π‘₯ + 1 2  = 1 2
  • B ο€Ό π‘₯ βˆ’ 1 4  = 1 2
  • C ο€Ό π‘₯ βˆ’ 1 2  = 3 4 2
  • D ο€Ό π‘₯ βˆ’ 1 2  = 1 2
  • E ο€Ό π‘₯ βˆ’ 1 4  = 3 4 2

Q10:

Escreva a equação π‘₯ βˆ’ 2 √ 3 π‘₯ + 1 = 0 2 na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž 2 .

  • A ο€» π‘₯ βˆ’ √ 3  = βˆ’ 2 2
  • B ( π‘₯ βˆ’ 3 ) = 2 2
  • C ο€» π‘₯ βˆ’ √ 3  = βˆ’ 1 2
  • D ο€» π‘₯ βˆ’ √ 3  = 2 2
  • E ( π‘₯ + 3 ) = 2 2

Q11:

Escreva a equação 3 π‘₯ + 𝑏 π‘₯ βˆ’ 1 = 0 2 na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž 2 .

  • A ο€½ π‘₯ + 𝑏 6  = 1 2
  • B ο€½ π‘₯ βˆ’ 𝑏 6  = 𝑏 + 1 2 3 6 2 2
  • C ο€Ύ π‘₯ + 𝑏 3 6  = 𝑏 + 1 2 3 6 2 2 2
  • D ο€½ π‘₯ + 𝑏 6  = 𝑏 + 1 2 3 6 2 2
  • E ο€Ύ π‘₯ βˆ’ 𝑏 3 6  = 𝑏 + 1 2 3 6 2 2 2

Q12:

Escreve a equação π‘₯ + 𝑏 π‘₯ + 𝑐 = 0 2 na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž 2 .

  • A ο€½ π‘₯ + 𝑏 2  = βˆ’ 𝑐 2
  • B ο€½ π‘₯ βˆ’ 𝑏 2  = 𝑏 βˆ’ 4 𝑐 4 2 2
  • C ο€Ύ π‘₯ + 𝑏 4  = 𝑏 βˆ’ 4 𝑐 4 2 2 2
  • D ο€½ π‘₯ + 𝑏 2  = 𝑏 βˆ’ 4 𝑐 4 2 2
  • E ο€½ π‘₯ + 𝑏 2  = 𝑏 + 4 𝑐 4 2 2

Q13:

Escreva a equação π‘Ž π‘₯ + 𝑏 π‘₯ + 𝑐 = 0  , em que π‘Ž β‰  0 , na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž  .

  • A ο€½ π‘₯ + 𝑏 2 π‘Ž  = βˆ’ 𝑐 π‘Ž 
  • B ο€½ π‘₯ βˆ’ 𝑏 2 π‘Ž  = 𝑏 βˆ’ 4 π‘Ž 𝑐 4 π‘Ž   
  • C ο€½ π‘₯ + 𝑏 2 π‘Ž  = 𝑏 βˆ’ π‘Ž 𝑐 π‘Ž   
  • D ο€½ π‘₯ + 𝑏 2 π‘Ž  = 𝑏 βˆ’ 4 π‘Ž 𝑐 4 π‘Ž   
  • E ο€½ π‘₯ βˆ’ 𝑏 2 π‘Ž  = βˆ’ 𝑐 π‘Ž 

Q14:

Qual das seguintes equaçáes pode ser transformada na equação 2 π‘₯ + 2 8 π‘₯ + 6 = 0  expandindo, rearranjando e multiplicando por um escalar?

  • A ( π‘₯ + 7 ) = βˆ’ 3 
  • B ( π‘₯ βˆ’ 7 ) = 4 6 
  • C ( π‘₯ + 4 9 ) = 4 6 
  • D ( π‘₯ + 7 ) = 4 6 
  • E ( π‘₯ + 4 9 ) = βˆ’ 3 

Q15:

Dado que π‘₯ βˆ’ π‘₯ βˆ’ 𝑐 = 0  pode ser escrito na forma ( π‘₯ βˆ’ 𝑝 ) = 3  , encontre o valor de 𝑐 .

  • A βˆ’ 1 3 4
  • B 1 3 4
  • C3
  • D 1 1 4
  • E βˆ’ 1 1 4

Q16:

Encontre os valores de π‘Ž para o qual a equação π‘₯ + 2 π‘Ž π‘₯ + π‘Ž + π‘Ž = π‘Ž    Γ© satisfeita por apenas um valor de π‘₯ .

  • A π‘Ž = 1 , π‘Ž = 0
  • B π‘Ž = 0 , π‘Ž = 1 βˆ’ √ 5 2 , π‘Ž = 1 + √ 5 2
  • C π‘Ž = 1 , π‘Ž = βˆ’ 1
  • D π‘Ž = 1 , π‘Ž = 0 , π‘Ž = βˆ’ 1
  • E π‘Ž = βˆ’ 2 + √ 5 , π‘Ž = 0 , π‘Ž = βˆ’ 2 + √ 5

Q17:

Dados que ( 3 π‘₯ βˆ’ 2 𝑦 ) = 6  e 9 π‘₯ + 4 𝑦 = 6   , encontre o valor de π‘₯ 𝑦 .

Q18:

Qual das seguintes equaçáes pode ser expandida e rearranjada para π‘₯ + 1 = 8 π‘₯  ?

  • A ( π‘₯ βˆ’ 4 ) = βˆ’ 1 5 
  • B ( π‘₯ + 4 ) = 1 5 
  • C ( π‘₯ + 4 ) = βˆ’ 1 5 
  • D ( π‘₯ βˆ’ 4 ) = 1 5 
  • E ( π‘₯ βˆ’ 8 ) = 1 5 

Q19:

Ao escrever π‘₯ + 2 π‘Ž π‘₯ + π‘Ž = 0  na forma ( π‘₯ βˆ’ 𝑝 ) = π‘ž  , determine quando a equação nΓ£o tem raΓ­zes reais.

  • A quando π‘Ž > 0
  • B quando π‘Ž < 0 ou π‘Ž > 0
  • C quando π‘Ž < 0
  • D quando 0 < π‘Ž < 1
  • E quando π‘Ž < 1

Q20:

Fatore completamente 2 4 π‘₯ 𝑦 + 3 π‘₯ + 4 8 𝑦  οŠͺ  .

  • A ( π‘₯ + 𝑦 )  
  • B ( π‘₯ + 4 𝑦 + 3 ) 
  • C 3 ( 4 π‘₯ + 𝑦 )  
  • D 3 ( π‘₯ + 4 𝑦 )  
  • E ( 4 π‘₯ + 𝑦 )  

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