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Worksheet: Solving Quadratics Using the Formula

Q1:

Find the solution set of π‘₯ + 8 π‘₯ + 1 8 5 = 0 2 given π‘₯ ∈ β„‚ .

  • A { 2 βˆ’ 3 𝑖 , 2 + 3 𝑖 }
  • B { βˆ’ 4 βˆ’ 6 𝑖 , βˆ’ 4 + 6 𝑖 }
  • C { 4 βˆ’ 6 𝑖 , 4 + 6 𝑖 }
  • D { βˆ’ 4 + 1 3 𝑖 , βˆ’ 4 βˆ’ 1 3 𝑖 }

Q2:

Find the solution set of βˆ’ 6 π‘₯ + 5 π‘₯ βˆ’ 5 = 0 2 over β„‚ .

  • A  2 5 1 2 βˆ’ √ 1 1 5 1 2 𝑖 , 2 5 1 2 + √ 1 1 5 1 2 𝑖 
  • B  5 1 2 βˆ’ √ 1 1 5 1 2 𝑖 , 5 1 2 + √ 1 1 5 1 2 𝑖 
  • C  βˆ’ 1 2 4 + √ 3 7 1 2 0 𝑖 , βˆ’ 1 2 4 βˆ’ √ 3 7 1 2 0 𝑖 
  • D  5 1 2 βˆ’ √ 9 5 1 2 𝑖 , 5 1 2 + √ 9 5 1 2 𝑖 

Q3:

Find the solution set of 5 π‘₯ + 6 π‘₯ + 9 = 0 2 over β„‚ .

  • A  βˆ’ 1 8 5 + √ 1 7 4 1 0 𝑖 , βˆ’ 1 8 5 βˆ’ √ 1 7 4 1 0 𝑖 
  • B  βˆ’ 3 5 + √ 1 7 4 1 0 𝑖 , βˆ’ 3 5 βˆ’ √ 1 7 4 1 0 𝑖 
  • C  βˆ’ 1 3 0 + √ 2 6 1 8 0 𝑖 , βˆ’ 1 3 0 βˆ’ √ 2 6 1 8 0 𝑖 
  • D  βˆ’ 3 5 βˆ’ 6 5 𝑖 , βˆ’ 3 5 + 6 5 𝑖 

Q4:

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

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

Q5:

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

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

Q6:

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‘˜ = 2 4 ,  βˆ’ 3 2 3 + √ 3 4 3 𝑖 , βˆ’ 3 2 3 βˆ’ √ 3 4 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‘˜ = 1 2 ,  βˆ’ 4 3 + 2 √ 5 3 𝑖 , βˆ’ 4 3 βˆ’ 2 √ 5 3 𝑖 

Q7:

Factor π‘₯ + 4 2 2 over the complex numbers.

  • A ( π‘₯ + √ 4 2 𝑖 ) ( π‘₯ + √ 4 2 𝑖 )
  • B ( π‘₯ + √ 4 2 ) ( π‘₯ βˆ’ √ 4 2 )
  • C ( π‘₯ βˆ’ √ 4 2 𝑖 ) ( π‘₯ βˆ’ √ 4 2 𝑖 )
  • D ( π‘₯ + √ 4 2 𝑖 ) ( π‘₯ βˆ’ √ 4 2 𝑖 )
  • E ( π‘₯ + √ 4 2 ) ( π‘₯ + √ 4 2 )

Q8:

The sum of the roots of the equation π‘₯ + π‘˜ π‘₯ + 7 = 0 2 is 1. Find the value of π‘˜ and the solution set of the equation.

  • A π‘˜ = βˆ’ 1 ,  1 2 + √ 6 2 𝑖 , 1 2 βˆ’ √ 6 2 𝑖 
  • B π‘˜ = 1 ,  βˆ’ 1 2 + 3 √ 3 2 𝑖 , βˆ’ 1 2 βˆ’ 3 √ 3 2 𝑖 
  • C π‘˜ = 1 ,  βˆ’ 1 2 + √ 6 2 𝑖 , βˆ’ 1 2 βˆ’ √ 6 2 𝑖 
  • D π‘˜ = βˆ’ 1 ,  1 2 + 3 √ 3 2 𝑖 , 1 2 βˆ’ 3 √ 3 2 𝑖 