Worksheet: Roots of Cubic Polynomials

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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 ( 𝑥 ) = 7 𝑥 ( 𝑥 − 1 ) ( 𝑥 + 6 ) .

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

Q2:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 + 5 𝑥 − 9 𝑥 − 4 5 .

  • A { 5 , 3 , − 3 }
  • B { − 5 , 3 }
  • C { − 5 , − 3 }
  • D { − 5 , 3 , − 3 }
  • E { 5 , 3 }

Q3:

Find the value of 𝑎 , given the set 𝑧 ( 𝑓 ) = { − 2 } contains the zero of the function 𝑓 ( 𝑥 ) = 𝑥 − 𝑥 + 𝑎 .

Q4:

Solve the equation ( 3 𝑥 − 2 ) ( 5 𝑥 + 2 ) ( 7 𝑥 − 3 ) = 0 .

  • A 𝑥 = 2 , 𝑥 = − 2 , 𝑥 = 3
  • B 𝑥 = − 2 3 , 𝑥 = 2 5 , 𝑥 = − 3 7
  • C 𝑥 = − 2 , 𝑥 = 2 , 𝑥 = − 3
  • D 𝑥 = 2 3 , 𝑥 = − 2 5 , 𝑥 = 3 7
  • E 𝑥 = 3 2 , 𝑥 = − 5 2 , 𝑥 = 7 3

Q5:

Solve the equation ( 𝑥 − 2 ) ( 𝑥 + 2 ) ( 𝑥 − 3 ) = 0 .

  • A 𝑥 = 2 , 𝑥 = 2 , 𝑥 = 3
  • B 𝑥 = − 2 , 𝑥 = 2 , 𝑥 = − 3
  • C 𝑥 = 2 , 𝑥 = 2 , 𝑥 = − 3
  • D 𝑥 = 2 , 𝑥 = − 2 , 𝑥 = 3
  • E 𝑥 = − 2 , 𝑥 = − 2 , 𝑥 = − 3

Q6:

Determine the solution set of the equation 𝑦 − 7 2 = − 5 1 2 in ℤ .

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

Q7:

Solve 𝑥 = 8 3 .

  • A 𝑥 = 2 4
  • B 𝑥 = 2 or 𝑥 = − 2
  • C 𝑥 = 2 4 or 𝑥 = − 2 4
  • D 𝑥 = 2
  • E 𝑥 = 3

Q8:

Solve 𝑥 + 1 0 = 7 4 3 .

  • A 𝑥 = 8
  • B 𝑥 = 4 or 𝑥 = − 4
  • C 𝑥 = 8 or 𝑥 = − 8
  • D 𝑥 = 4
  • E 𝑥 = 9

Q9:

Find the solution set of 8 1 𝑥 = 1 2 1 𝑥 in ℝ .

  • A 1 1 9
  • B 1 1 9 , − 1 1 9
  • C 0 , 9 1 1 , − 9 1 1
  • D 0 , 1 1 9 , − 1 1 9
  • E 9 1 1 , − 9 1 1

Q10:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 ( 𝑥 − 2 ) ( 𝑥 − 7 ) .

  • A 0 , 7 , 1 2
  • B { 0 , − 7 , − 2 }
  • C { − 1 , 7 , 2 }
  • D { 0 , 7 , 2 }
  • E { 7 , 2 }

Q11:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 − 4 𝑥 − 9 𝑥 + 3 6 .

  • A { − 4 , 3 , − 3 }
  • B { 4 , 3 }
  • C { 4 , − 3 }
  • D { 4 , 3 , − 3 }
  • E { − 4 , 3 }

Q12:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 − 2 𝑥 − 6 𝑥 + 2 7 .

  • A { 0 }
  • B { 3 }
  • C ∅
  • D { − 3 }
  • E { 0 , − 3 }

Q13:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 − 2 𝑥 − 1 6 𝑥 + 3 2 .

  • A { − 2 , 4 , − 4 }
  • B { 2 , 4 }
  • C { 2 , − 4 }
  • D { 2 , 4 , − 4 }
  • E { − 2 , 4 }

Q14:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 − 2 𝑥 − 2 5 𝑥 + 5 0 .

  • A { − 2 , 5 , − 5 }
  • B { 2 , 5 }
  • C { 2 , − 5 }
  • D { 2 , 5 , − 5 }
  • E { − 2 , 5 }

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