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Lesson: Using the Quadratic Formula to Solve Quadratic Equations with Two Complex Roots

Sample Question Videos

Worksheet • 8 Questions • 1 Video

Q1:

Solve the quadratic equation π‘₯ + π‘₯ + 1 = 0 2 .

  • A π‘₯ = βˆ’ 1 + √ 3 𝑖 2 , π‘₯ = βˆ’ 1 βˆ’ √ 3 𝑖 2
  • B π‘₯ = βˆ’ 1 + √ 3 𝑖 , π‘₯ = βˆ’ 1 βˆ’ √ 3 𝑖
  • C π‘₯ = 1 + √ 3 𝑖 2 , π‘₯ = 1 βˆ’ √ 3 𝑖 2
  • D π‘₯ = βˆ’ 1 + √ 5 2 , π‘₯ = βˆ’ 1 βˆ’ √ 5 2
  • E π‘₯ = 1 + √ 5 2 , π‘₯ = 1 βˆ’ √ 5 2

Q2:

Solve the quadratic equation 4 π‘₯ + 3 π‘₯ + 1 = 0 2 .

  • A π‘₯ = βˆ’ 3 + √ 7 𝑖 8 , π‘₯ = βˆ’ 3 βˆ’ √ 7 𝑖 8
  • B π‘₯ = βˆ’ 3 + √ 7 𝑖 4 , π‘₯ = βˆ’ 3 βˆ’ √ 7 𝑖 4
  • C π‘₯ = 3 + √ 7 𝑖 8 , π‘₯ = 3 βˆ’ √ 7 𝑖 8
  • D π‘₯ = βˆ’ 3 + √ 5 2 , π‘₯ = βˆ’ 3 βˆ’ √ 5 2
  • E π‘₯ = 1 , π‘₯ = βˆ’ 1 4

Q3:

The product of the roots of the equation 3 π‘₯ + 8 π‘₯ + π‘˜ = 0 2 is 4. Find the value of π‘˜ and the solution set of the equation.

  • A π‘˜ = 1 2 ,  βˆ’ 4 3 + 2 √ 5 3 𝑖 , βˆ’ 4 3 βˆ’ 2 √ 5 3 𝑖 
  • B π‘˜ = 4 3 ,  βˆ’ 4 3 + √ 3 4 3 𝑖 , βˆ’ 4 3 βˆ’ √ 3 4 3 𝑖 
  • C π‘˜ = 4 ,  βˆ’ 1 1 8 + √ 5 8 1 4 4 𝑖 , βˆ’ 1 1 8 βˆ’ √ 5 8 1 4 4 𝑖 
  • D π‘˜ = 2 4 ,  βˆ’ 3 2 3 + √ 3 4 3 𝑖 , βˆ’ 3 2 3 βˆ’ √ 3 4 3 𝑖 
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