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Worksheet: Roots of Cubic Polynomials

In this worksheet, we will practice finding the roots of cubic polynomials with integer coefficients.

Q1:

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

  • A { βˆ’ 7 , βˆ’ 6 , 1 }
  • B { 0 , 6 , βˆ’ 1 }
  • C { βˆ’ 6 , 1 }
  • D { 0 , βˆ’ 6 , 1 }

Q2:

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

  • A  0 , 7 , 1 2 
  • B { 0 , βˆ’ 7 , βˆ’ 2 }
  • C { βˆ’ 1 , 7 , 2 }
  • D { 0 , 7 , 2 }
  • E { 7 , 2 }

Q3:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = 3 π‘₯ + 9 π‘₯ 3 2 .

  • A { 3 , 0 }
  • B { βˆ’ 3 }
  • C { 3 }
  • D { βˆ’ 3 , 0 }
  • E  βˆ’ 1 3 , 0 

Q4:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = 7 π‘₯ βˆ’ π‘₯ 3 2 .

  • A  βˆ’ 1 7 , 0 
  • B  1 7 
  • C  βˆ’ 1 7 
  • D  1 7 , 0 
  • E { 7 , 0 }

Q5:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = 2 π‘₯ + 1 5 π‘₯ + 2 7 π‘₯ 3 2 .

  • A  βˆ’ 9 2 , 3 , 0 
  • B  βˆ’ 9 2 , βˆ’ 3 
  • C  9 2 , βˆ’ 3 , 0 
  • D  βˆ’ 9 2 , βˆ’ 3 , 0 
  • E  9 2 , 3 , 0 

Q6:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = π‘₯ + 5 π‘₯ βˆ’ 9 π‘₯ βˆ’ 4 5 3 2 .

  • A { 5 , 3 , βˆ’ 3 }
  • B { βˆ’ 5 , 3 }
  • C { βˆ’ 5 , βˆ’ 3 }
  • D { βˆ’ 5 , 3 , βˆ’ 3 }
  • E { 5 , 3 }

Q7:

Find the set of zeros of the function 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 4 π‘₯ βˆ’ 9 π‘₯ + 3 6 3 2 .

  • A { βˆ’ 4 , 3 , βˆ’ 3 }
  • B { 4 , 3 }
  • C { 4 , βˆ’ 3 }
  • D { 4 , 3 , βˆ’ 3 }
  • E { βˆ’ 4 , 3 }

Q8:

Solve π‘₯ = 8 3 .

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

Q9:

Find the value of π‘Ž , given the set 𝑧 ( 𝑓 ) = { βˆ’ 2 } contains the zero of the function 𝑓 ( π‘₯ ) = π‘₯ βˆ’ π‘₯ + π‘Ž 3 2 .

Q10:

Determine the solution set of the equation ο€Ή 𝑦 βˆ’ 7 2  = βˆ’ 5 1 2 2 3 in β„€ .

  • A { 8 }
  • B { βˆ’ 8 }
  • C { 6 4 }
  • D { βˆ’ 8 , 8 }
  • E { βˆ’ 8 0 }

Q11:

Solve the equation ( 3 π‘₯ βˆ’ 2 ) ( 5 π‘₯ + 2 ) ( 7 π‘₯ βˆ’ 3 ) = 0 .

  • A π‘₯ = 2 , π‘₯ = βˆ’ 2 , π‘₯ = 3
  • B π‘₯ = βˆ’ 2 3 , π‘₯ = 2 5 , π‘₯ = βˆ’ 3 7
  • C π‘₯ = βˆ’ 2 , π‘₯ = 2 , π‘₯ = βˆ’ 3
  • D π‘₯ = 2 3 , π‘₯ = βˆ’ 2 5 , π‘₯ = 3 7
  • E π‘₯ = 3 2 , π‘₯ = βˆ’ 5 2 , π‘₯ = 7 3

Q12:

Find the solution set of 8 1 π‘₯ = 1 2 1 π‘₯ 3 in ℝ .

  • A  1 1 9 
  • B  1 1 9 , βˆ’ 1 1 9 
  • C  0 , 9 1 1 , βˆ’ 9 1 1 
  • D  0 , 1 1 9 , βˆ’ 1 1 9 
  • E  9 1 1 , βˆ’ 9 1 1 

Q13:

Solve the equation ( π‘₯ βˆ’ 2 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 3 ) = 0 .

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

Q14:

Solve π‘₯ + 1 0 = 7 4 3 .

  • A π‘₯ = 8
  • B π‘₯ = 4 or π‘₯ = βˆ’ 4
  • C π‘₯ = 8 or π‘₯ = βˆ’ 8
  • D π‘₯ = 4
  • E π‘₯ = 9

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