Atividade: Equações Polinomiais de Grau Superior

Nesta atividade, nós vamos praticar a utilização de estratégias diferentes para resolver equações polinomiais de grau maior que dois.

Q1:

Resolva a equação ( 3 π‘₯ βˆ’ 1 ) ( 5 π‘₯ + 6 ) ( 3 π‘₯ βˆ’ 4 ) ( 8 π‘₯ + 7 ) = 0 .

  • A π‘₯ = 1 , π‘₯ = βˆ’ 6 , π‘₯ = 4 , π‘₯ = βˆ’ 7
  • B π‘₯ = βˆ’ 1 3 , π‘₯ = 6 5 , π‘₯ = βˆ’ 4 3 , π‘₯ = 7 8
  • C π‘₯ = βˆ’ 1 , π‘₯ = 6 , π‘₯ = βˆ’ 4 , π‘₯ = 7
  • D π‘₯ = 1 3 , π‘₯ = βˆ’ 6 5 , π‘₯ = 4 3 , π‘₯ = βˆ’ 7 8
  • E π‘₯ = 3 , π‘₯ = βˆ’ 5 6 , π‘₯ = 3 4 , π‘₯ = βˆ’ 8 7

Q2:

Qual das seguintes opçáes Γ© uma forma fatorizada de π‘₯ + 2 π‘₯ βˆ’ 1 6 π‘₯ βˆ’ 3 2 3 2 ?

  • A ( π‘₯ βˆ’ 4 ) ( π‘₯ + 2 ) 2
  • B ( π‘₯ + 4 ) ( π‘₯ βˆ’ 2 ) 2
  • C ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) ( π‘₯ βˆ’ 2 )
  • D ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) ( π‘₯ + 2 )
  • E ( π‘₯ + 4 ) ( π‘₯ + 2 )

Q3:

Sendo 𝑓 ( π‘₯ ) = π‘₯ + 3 π‘₯ βˆ’ 1 3 π‘₯ βˆ’ 1 5 3 2 e 𝑓 ( βˆ’ 1 ) = 0 , determine as outras raΓ­zes de 𝑓 ( π‘₯ ) .

  • A π‘₯ = βˆ’ 3 , π‘₯ = βˆ’ 5
  • B π‘₯ = βˆ’ 3 , π‘₯ = 5
  • C π‘₯ = βˆ’ 2 , π‘₯ = βˆ’ 6
  • D π‘₯ = 3 , π‘₯ = βˆ’ 5
  • E π‘₯ = 2 , π‘₯ = 6

Q4:

Por fatoração, encontre todas as soluçáes para π‘₯ + 2 π‘₯ βˆ’ 1 7 π‘₯ βˆ’ 1 8 π‘₯ + 7 2 = 0 4 3 2 , dado que ( π‘₯ βˆ’ 3 ) e ( π‘₯ + 4 ) sΓ£o fatores de π‘₯ + 2 π‘₯ βˆ’ 1 7 π‘₯ βˆ’ 1 8 π‘₯ + 7 2 4 3 2 .

  • A π‘₯ = βˆ’ 3 , π‘₯ = βˆ’ 4 , π‘₯ = βˆ’ 2 , π‘₯ = 3
  • B π‘₯ = βˆ’ 3 , π‘₯ = 4 , π‘₯ = βˆ’ 2 , π‘₯ = 3
  • C π‘₯ = 3 , π‘₯ = 4 , π‘₯ = 2 , π‘₯ = βˆ’ 3
  • D π‘₯ = 3 , π‘₯ = βˆ’ 4 , π‘₯ = 2 , π‘₯ = βˆ’ 3
  • E π‘₯ = 3 , π‘₯ = βˆ’ 4 , π‘₯ = βˆ’ 2

Q5:

Determine os valores de π‘Ž , 𝑏 , e 𝑐 sabendo que ( π‘₯ + 3 ) , ( π‘₯ βˆ’ 2 ) , e ( π‘₯ + 4 ) sΓ£o fatores de π‘₯ + π‘Ž π‘₯ + 𝑏 π‘₯ + 𝑐 3 2 .

  • A π‘Ž = 5 , 𝑏 = 2 , 𝑐 = βˆ’ 2 4
  • B π‘Ž = βˆ’ 5 , 𝑏 = βˆ’ 2 , 𝑐 = βˆ’ 2 4
  • C π‘Ž = 5 , 𝑏 = βˆ’ 2 , 𝑐 = 2 4
  • D π‘Ž = 5 , 𝑏 = βˆ’ 2 , 𝑐 = βˆ’ 2 4
  • E π‘Ž = βˆ’ 5 , 𝑏 = 2 , 𝑐 = 2 4

Q6:

Quantas raΓ­zes tem o polinΓ³mio 3 π‘₯ βˆ’ 2 π‘₯ + π‘₯ + 4 π‘₯ βˆ’ 2 6 3 2 ?

Q7:

Resolva a equação ( π‘₯ βˆ’ 1 ) ( π‘₯ + 6 ) ( π‘₯ βˆ’ 4 ) ( π‘₯ + 7 ) = 0 .

  • A π‘₯ = βˆ’ 1 , π‘₯ = βˆ’ 6 , π‘₯ = βˆ’ 4 , π‘₯ = βˆ’ 7
  • B π‘₯ = βˆ’ 1 , π‘₯ = 6 , π‘₯ = βˆ’ 4 , π‘₯ = 7
  • C π‘₯ = 1 , π‘₯ = 6 , π‘₯ = 4 , π‘₯ = 7
  • D π‘₯ = 1 , π‘₯ = βˆ’ 6 , π‘₯ = 4 , π‘₯ = βˆ’ 7
  • E π‘₯ = 1 , π‘₯ = βˆ’ 6 , π‘₯ = βˆ’ 4 , π‘₯ = βˆ’ 7

Q8:

Fatore a expressΓ£o 4 𝑐 βˆ’ 2 8 βˆ’ 6 𝑐 6 3 completamente.

  • A 2 ο€Ή 2 𝑐 + 7  ο€Ή 𝑐 βˆ’ 2  3 3
  • B 2 ο€Ή 𝑐 βˆ’ 7  ο€Ή 2 𝑐 + 2  3 3
  • C ο€Ή 4 𝑐 βˆ’ 1 4  ο€Ή 𝑐 βˆ’ 2  3 3
  • D 2 ο€Ή 2 𝑐 βˆ’ 7  ο€Ή 𝑐 + 2  3 3
  • E ο€Ή 2 𝑐 + 7  ο€Ή 2 𝑐 + 4  3 3

Q9:

Fatore a expressΓ£o 7 5 𝑏 π‘š + 6 0 𝑏 π‘š + 1 2 𝑏 οŠͺ  completamente.

  • A 3 𝑏 ( 5 π‘š βˆ’ 2 ) 
  • B 5 𝑏 ο€Ή 5 π‘š βˆ’ 2   
  • C 𝑏 ( 5 π‘š + 2 ) 
  • D 3 𝑏 ο€Ή 5 π‘š + 2   
  • E 𝑏 ο€Ή 5 π‘š βˆ’ 2   

Q10:

Determine o conjunto-solução de π‘₯ βˆ’ 2 5 π‘₯ + 1 4 4 = 0 οŠͺ  em ℝ .

  • A { 8 , βˆ’ 8 , 1 8 , βˆ’ 1 8 }
  • B { βˆ’ 1 6 , βˆ’ 9 }
  • C { βˆ’ 8 , βˆ’ 1 8 }
  • D { 4 , βˆ’ 4 , 3 , βˆ’ 3 }
  • E { 4 , 3 }

Q11:

Dado que π‘₯ pertence a ℝ , determine o valor de π‘₯ que satisfaz a seguinte equação ο€Ή 3 π‘₯ βˆ’ 6  ο€Ή π‘₯ + 9  = 0   . Apresente a resposta arredondada Γ s centΓ©simas.

Q12:

Determine o conjunto-solução da equação ο€Ή π‘₯ βˆ’ 5 0 6  ο€Ή π‘₯ βˆ’ 5 8  = 0   em ℝ .

  • A  √ 5 8 , βˆ’ √ 5 8 , βˆ’ √ 5 0 6  
  • B  √ 5 8 , √ 5 0 6  
  • C  βˆ’ √ 5 8 , βˆ’ √ 5 0 6  
  • D  √ 5 8 , βˆ’ √ 5 8 , √ 5 0 6  
  • E  √ 5 0 6 , βˆ’ √ 5 0 6 , √ 5 8  

Q13:

Quantas raΓ­zes tem a equação π‘₯ + π‘₯ = 7 2 ?

A Nagwa usa cookies para garantir que vocΓͺ tenha a melhor experiΓͺncia em nosso site. Saiba mais sobre nossa PolΓ­tica de privacidade.