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Lesson: Zeros of Polynomial Functions

Sample Question Videos

Worksheet • 9 Questions • 3 Videos

Q1:

If the set of zeros of the function 𝑓 ( π‘₯ ) = π‘₯ + 𝑏 π‘₯ + 3 4 3 2 3 is { βˆ’ 8 , 8 } , find the value of 𝑏 .

Q2:

Find, by factoring, the zeros of the function 𝑓 ( π‘₯ ) = π‘₯ + 2 π‘₯ βˆ’ 3 5 2 .

  • A βˆ’ 7 , 5
  • B βˆ’ 6 , 8
  • C βˆ’ 5 , 7
  • D 5 , 7
  • E βˆ’ 7 , βˆ’ 5

Q3:

Find, by factoring, the zeros of the function 𝑓 ( 𝑦 ) = 𝑦 + 8 𝑦 + 7 2 .

  • A βˆ’ 7 , βˆ’ 1
  • B βˆ’ 8 , 1
  • C 7 , 1
  • D βˆ’ 1 , 8
  • E βˆ’ 7 , 1

Q4:

Find all the zeros of 𝑓 ( π‘₯ ) = π‘₯ + 5 π‘₯ βˆ’ 9 π‘₯ βˆ’ 4 5 3 2 and state their multiplicities.

  • A π‘₯ = βˆ’ 3 with multiplicity 1, π‘₯ = βˆ’ 5 with multiplicity 1, π‘₯ = 3 with multiplicity 1
  • B π‘₯ = βˆ’ 3 with multiplicity 2, π‘₯ = 3 with multiplicity 2
  • C π‘₯ = βˆ’ 5 with multiplicity 1, π‘₯ = 3 with multiplicity 2
  • D π‘₯ = βˆ’ 3 with multiplicity 1, π‘₯ = βˆ’ 5 with multiplicity 1

Q5:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = 1 3 ( π‘₯ βˆ’ 4 ) .

  • A { 4 }
  • B { βˆ’ 4 }
  • C  1 3 , 4 
  • D  1 3 , βˆ’ 4 

Q6:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = ( π‘₯ βˆ’ 8 ) ( π‘₯ + 1 0 ) 2 .

  • A { 8 , βˆ’ 1 0 }
  • B { βˆ’ 1 0 , βˆ’ 8 , 8 }
  • C { βˆ’ 8 , 1 0 }
  • D { βˆ’ 1 0 , βˆ’ 8 }
  • E { 8 , 1 0 }

Q7:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 1 7 π‘₯ + 1 6 4 2 .

  • A { βˆ’ 4 , βˆ’ 1 , 1 , 4 }
  • B { βˆ’ 4 , βˆ’ 1 }
  • C { 1 , 4 }
  • D { 4 }
  • E { 1 }

Q8:

The function 𝑓 ( π‘₯ ) = π‘Ž π‘₯ + 5 4 π‘₯ + 8 1   and the function 𝑔 ( π‘₯ ) = π‘Ž π‘₯ + 9 have the same set of zeros. Find π‘Ž and the set of zeros.

  • A π‘Ž = 3 , 𝑧 ( 𝑓 ) = { βˆ’ 3 }
  • B π‘Ž = 3 , 𝑧 ( 𝑓 ) =  βˆ’ 1 3 
  • C π‘Ž = 3 , 𝑧 ( 𝑓 ) = { 3 }
  • D π‘Ž = 9 , 𝑧 ( 𝑓 ) = { 3 }
  • E π‘Ž = 9 , 𝑧 ( 𝑓 ) = { βˆ’ 3 }

Q9:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 1 π‘₯ βˆ’ 4 2 .

  • A { 1 }
  • B ℝ βˆ’ { βˆ’ 2 , 2 }
  • C { βˆ’ 2 , 2 }
  • D ℝ βˆ’ { 1 }
  • E { βˆ’ 2 , 1 , 2 }
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