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Lesson: Writing a Polynomial Function given Zeros

Sample Question Videos

Worksheet • 16 Questions • 2 Videos

Q1:

Find, in its simplest form, the quadratic equation whose roots are βˆ’ 3 and βˆ’ 8 .

  • A π‘₯ + 1 1 π‘₯ + 2 4 = 0 2
  • B π‘₯ βˆ’ 2 4 π‘₯ βˆ’ 1 1 = 0 2
  • C π‘₯ + 2 4 π‘₯ + 1 1 = 0 2
  • D π‘₯ + 1 1 π‘₯ βˆ’ 2 4 = 0 2
  • E π‘₯ βˆ’ 1 1 π‘₯ + 2 4 = 0 2

Q2:

Find, in its simplest form, the quadratic equation whose roots are βˆ’ 1 4 𝑖 and 1 4 𝑖 .

  • A π‘₯ + 1 9 6 = 0 2
  • B π‘₯ βˆ’ 1 9 6 = 0 2
  • C π‘₯ βˆ’ 2 8 = 0 2
  • D π‘₯ + 2 8 = 0 2

Q3:

Find, in its simplest form, the quadratic equation whose roots are βˆ’ 4 + 5 𝑖 and βˆ’ 4 βˆ’ 5 𝑖 .

  • A π‘₯ + 8 π‘₯ + 4 1 = 0 2
  • B π‘₯ βˆ’ 8 π‘₯ βˆ’ 9 = 0 2
  • C π‘₯ βˆ’ 8 π‘₯ + 4 1 = 0 2
  • D π‘₯ + 8 π‘₯ βˆ’ 9 = 0 2
  • E π‘₯ βˆ’ 8 π‘₯ βˆ’ 4 1 = 0 2

Q4:

Which quadratic equation has roots π‘₯ = 2 Β± 𝑖 ?

  • A π‘₯ βˆ’ 4 π‘₯ + 5 = 0 2
  • B π‘₯ βˆ’ 5 π‘₯ + 4 = 0 2
  • C π‘₯ + 4 π‘₯ + 5 = 0 2
  • D π‘₯ + 4 π‘₯ + 3 = 0 2
  • E π‘₯ βˆ’ 4 π‘₯ + 3 = 0 2

Q5:

Find, in its simplest form, the quadratic equation whose roots are 7 2 and 2 7 .

  • A 1 4 π‘₯ βˆ’ 5 3 π‘₯ + 1 4 = 0 2
  • B 1 4 π‘₯ βˆ’ 5 3 π‘₯ + 5 3 = 0 2
  • C 1 4 π‘₯ + 5 3 π‘₯ + 1 4 = 0 2
  • D 5 3 π‘₯ + 1 4 π‘₯ + 5 3 = 0 2
  • E 5 3 π‘₯ βˆ’ 1 4 π‘₯ + 5 3 = 0 2

Q6:

Find, in its simplest form, the quadratic equation whose roots are 5 + √ 2 and 5 βˆ’ √ 2 .

  • A π‘₯ βˆ’ 1 0 π‘₯ + 2 3 = 0 2
  • B π‘₯ + 1 0 π‘₯ + 2 7 = 0 2
  • C π‘₯ βˆ’ 1 0 π‘₯ + 2 1 = 0 2
  • D π‘₯ βˆ’ 1 0 π‘₯ + 2 7 = 0 2
  • E π‘₯ + 1 0 π‘₯ + 2 3 = 0 2

Q7:

Find, in its simplest form, the quadratic equation whose roots are βˆ’ 2 √ 5 + 3 and βˆ’ 2 √ 5 βˆ’ 3 .

  • A π‘₯ + 4 √ 5 π‘₯ + 1 1 = 0 2
  • B π‘₯ + 4 π‘₯ + 1 1 = 0 2
  • C π‘₯ βˆ’ 4 √ 5 π‘₯ + 1 1 = 0 2
  • D π‘₯ βˆ’ 4 √ 5 π‘₯ βˆ’ 1 9 = 0 2
  • E π‘₯ + 4 √ 5 π‘₯ + 1 7 = 0 2

Q8:

Find, in its simplest form, the quadratic equation whose roots are 2 + 3 √ 7 𝑖 and 2 βˆ’ 3 √ 7 𝑖 .

  • A π‘₯ βˆ’ 4 π‘₯ + 6 7 = 0 2
  • B π‘₯ + 4 √ 7 π‘₯ + 6 7 = 0 2
  • C π‘₯ + 4 π‘₯ + 6 7 = 0 2
  • D π‘₯ βˆ’ 4 π‘₯ βˆ’ 5 9 𝑖 = 0 2
  • E π‘₯ βˆ’ 4 π‘₯ βˆ’ 5 9 = 0 2

Q9:

Find, in its simplest form, the quadratic equation whose roots are 2 + 2 𝑖 βˆ’ 1 + 𝑖 and 2 + 4 𝑖 2 βˆ’ 𝑖 .

  • A π‘₯ + 4 = 0 2
  • B π‘₯ + 4 𝑖 = 0 2
  • C π‘₯ + 4 π‘₯ = 0 2
  • D π‘₯ βˆ’ 4 = 0 2

Q10:

Find, in its simplest form, the quadratic equation whose roots are 2 and 8.

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

Q11:

Find, in its simplest form, the quadratic equation whose roots are 9 βˆ’ 1 2 𝑖 and 9 + 1 2 𝑖 .

  • A π‘₯ βˆ’ 1 8 π‘₯ + 2 2 5 = 0 2
  • B π‘₯ + 1 8 π‘₯ βˆ’ 6 3 = 0 2
  • C π‘₯ + 1 8 π‘₯ + 2 2 5 = 0 2
  • D π‘₯ βˆ’ 1 8 π‘₯ βˆ’ 6 3 = 0 2
  • E π‘₯ + 1 8 π‘₯ βˆ’ 2 2 5 = 0 2

Q12:

Find, in its simplest form, the quadratic equation whose roots are 1 2 𝑖 and βˆ’ 1 2 𝑖 .

  • A π‘₯ + 1 4 4 = 0 2
  • B π‘₯ βˆ’ 1 4 4 = 0 2
  • C π‘₯ βˆ’ 2 4 = 0 2
  • D π‘₯ + 2 4 = 0 2

Q13:

Find, in its simplest form, the quadratic equation whose roots are 1 + √ 5 and 1 βˆ’ √ 5 .

  • A π‘₯ βˆ’ 2 π‘₯ βˆ’ 4 = 0 2
  • B π‘₯ + 2 π‘₯ + 6 = 0 2
  • C π‘₯ βˆ’ 2 π‘₯ βˆ’ 2 4 = 0 2
  • D π‘₯ βˆ’ 2 π‘₯ + 6 = 0 2
  • E π‘₯ + 2 π‘₯ βˆ’ 4 = 0 2

Q14:

Find, in its simplest form, the quadratic equation whose roots are 2 √ 2 + 6 and 2 √ 2 βˆ’ 6 .

  • A π‘₯ βˆ’ 4 √ 2 π‘₯ βˆ’ 2 8 = 0 2
  • B π‘₯ βˆ’ 4 π‘₯ βˆ’ 2 8 = 0 2
  • C π‘₯ + 4 √ 2 π‘₯ βˆ’ 2 8 = 0 2
  • D π‘₯ + 4 √ 2 π‘₯ βˆ’ 3 2 = 0 2
  • E π‘₯ βˆ’ 4 √ 2 π‘₯ + 2 = 0 2

Q15:

Find, in its simplest form, the quadratic equation whose roots are 6 7 and 7 6 .

  • A 4 2 π‘₯ βˆ’ 8 5 π‘₯ + 4 2 = 0 2
  • B 4 2 π‘₯ βˆ’ 8 5 π‘₯ + 8 5 = 0 2
  • C 4 2 π‘₯ + 8 5 π‘₯ + 4 2 = 0 2
  • D 8 5 π‘₯ + 4 2 π‘₯ + 8 5 = 0 2
  • E 8 5 π‘₯ βˆ’ 4 2 π‘₯ + 8 5 = 0 2

Q16:

Find, in its simplest form, the quadratic equation whose roots are βˆ’ 3 5 and βˆ’ 5 3 .

  • A 1 5 π‘₯ + 3 4 π‘₯ + 1 5 = 0 2
  • B 1 5 π‘₯ + 3 4 π‘₯ βˆ’ 3 4 = 0 2
  • C 1 5 π‘₯ βˆ’ 3 4 π‘₯ + 1 5 = 0 2
  • D βˆ’ 3 4 π‘₯ + 1 5 π‘₯ βˆ’ 3 4 = 0 2
  • E βˆ’ 3 4 π‘₯ βˆ’ 1 5 π‘₯ βˆ’ 3 4 = 0 2
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