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Worksheet: Solving Quadratics Using the Formula

Q1:

Solve the equation βˆ’ π‘₯ + 7 π‘₯ + 1 = 0 2 .

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

Q2:

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

  • A  9 βˆ’ √ 1 4 3 1 0 , 9 + √ 1 4 3 1 0 
  • B  3 βˆ’ √ 1 4 3 1 0 , 3 + √ 1 4 3 1 0 
  • C  3 βˆ’ √ 1 9 1 4 0 , 3 + √ 1 9 1 4 0 
  • D  3 βˆ’ √ 1 4 9 1 0 , 3 + √ 1 4 9 1 0 
  • E  βˆ’ 3 + √ 1 4 9 1 4 , βˆ’ 3 βˆ’ √ 1 4 9 1 4 

Q3:

Solve the equation βˆ’ π‘₯ + 8 π‘₯ βˆ’ 1 = 0 2 .

  • A { 3 1 , 3 3 }
  • B { 3 , 5 }
  • C  βˆ’ 8 + √ 6 6 2 , βˆ’ 8 βˆ’ √ 6 6 2 
  • D  4 βˆ’ √ 1 5 , 4 + √ 1 5 

Q4:

Solve the equation 2 π‘₯ + 3 π‘₯ βˆ’ 1 = 0 2 .

  • A  βˆ’ 9 + √ 1 1 4 , βˆ’ 9 βˆ’ √ 1 1 4 
  • B  βˆ’ 3 + √ 1 1 4 , βˆ’ 3 βˆ’ √ 1 1 4 
  • C  3 βˆ’ √ 5 8 , 3 + √ 5 8 
  • D  βˆ’ 3 + √ 1 7 4 , βˆ’ 3 βˆ’ √ 1 7 4 
  • E  3 βˆ’ √ 1 7 2 , 3 + √ 1 7 2 

Q5:

Solve the equation βˆ’ 2 π‘₯ + 9 π‘₯ + 3 = 0 2 .

  • A  8 1 βˆ’ √ 3 3 4 , 8 1 + √ 3 3 4 
  • B  9 βˆ’ √ 3 3 4 , 9 + √ 3 3 4 
  • C  9 βˆ’ √ 8 5 2 4 , 9 + √ 8 5 2 4 
  • D  9 βˆ’ √ 1 0 5 4 , 9 + √ 1 0 5 4 
  • E  βˆ’ 9 + √ 1 0 5 6 , βˆ’ 9 βˆ’ √ 1 0 5 6 

Q6:

Solve the equation βˆ’ 2 π‘₯ + 9 π‘₯ + 2 = 0 2 .

  • A  1 9 , 4 3 2 
  • B  1 , 7 2 
  • C  9 βˆ’ √ 8 5 1 6 , 9 + √ 8 5 1 6 
  • D  9 βˆ’ √ 9 7 4 , 9 + √ 9 7 4 
  • E  βˆ’ 9 + √ 9 7 4 , βˆ’ 9 βˆ’ √ 9 7 4 

Q7:

Solve the equation 7 π‘₯ + 8 π‘₯ βˆ’ 1 = 0 2 .

  • A  βˆ’ 2 9 7 , βˆ’ 5 
  • B  βˆ’ 1 7 , βˆ’ 1 
  • C  8 βˆ’ 5 √ 2 2 8 , 8 + 5 √ 2 2 8 
  • D  βˆ’ 4 + √ 2 3 7 , βˆ’ 4 βˆ’ √ 2 3 7 
  • E  4 βˆ’ √ 2 3 , 4 + √ 2 3 

Q8:

Solve the equation 8 π‘₯ + 9 π‘₯ βˆ’ 5 = 0 2 .

  • A  βˆ’ 1 7 4 , βˆ’ 4 7 8 
  • B  1 4 , βˆ’ 1 1 8 
  • C  9 βˆ’ √ 6 5 1 6 0 , 9 + √ 6 5 1 6 0 
  • D  βˆ’ 9 + √ 2 4 1 1 6 , βˆ’ 9 βˆ’ √ 2 4 1 1 6 
  • E  9 βˆ’ √ 2 4 1 1 0 , 9 + √ 2 4 1 1 0 

Q9:

Solve the equation 3 π‘₯ + 8 π‘₯ βˆ’ 4 = 0 2 .

  • A  βˆ’ 3 2 + √ 1 4 3 , βˆ’ 3 2 βˆ’ √ 1 4 3 
  • B  βˆ’ 4 + √ 1 4 3 , βˆ’ 4 βˆ’ √ 1 4 3 
  • C  8 βˆ’ √ 5 8 4 8 , 8 + √ 5 8 4 8 
  • D  βˆ’ 4 + 2 √ 7 3 , βˆ’ 4 βˆ’ 2 √ 7 3 
  • E  8 βˆ’ 4 √ 7 8 , 8 + 4 √ 7 8 

Q10:

Solve the equation π‘₯ + 8 π‘₯ βˆ’ 4 = 0 2 .

  • A  βˆ’ 3 2 + √ 6 , βˆ’ 3 2 βˆ’ √ 6 
  • B  βˆ’ 4 + √ 6 , βˆ’ 4 βˆ’ √ 6 
  • C  8 βˆ’ √ 6 2 1 6 , 8 + √ 6 2 1 6 
  • D  βˆ’ 4 + 2 √ 5 , βˆ’ 4 βˆ’ 2 √ 5 
  • E  8 βˆ’ 4 √ 5 8 , 8 + 4 √ 5 8 

Q11:

Solve the equation 7 π‘₯ + 9 π‘₯ βˆ’ 3 = 0 2 .

  • A  βˆ’ 8 1 + √ 9 3 1 4 , βˆ’ 8 1 βˆ’ √ 9 3 1 4 
  • B  βˆ’ 9 + √ 9 3 1 4 , βˆ’ 9 βˆ’ √ 9 3 1 4 
  • C  9 βˆ’ √ 6 7 8 4 , 9 + √ 6 7 8 4 
  • D  βˆ’ 9 + √ 1 6 5 1 4 , βˆ’ 9 βˆ’ √ 1 6 5 1 4 
  • E  9 βˆ’ √ 1 6 5 6 , 9 + √ 1 6 5 6 

Q12:

Find the solution set of the equation π‘₯ βˆ’ 3 π‘₯ + 1 = 0 2 , giving values correct to two decimal places.

  • A { 5 . 2 4 , 0 . 7 6 }
  • B { βˆ’ 2 . 6 2 , βˆ’ 0 . 3 8 }
  • C { βˆ’ 5 . 2 4 , βˆ’ 0 . 7 6 }
  • D { 2 . 6 2 , 0 . 3 8 }
  • E { 3 . 1 2 , βˆ’ 0 . 1 2 }

Q13:

Find the solution set of the equation π‘₯ 3 + 2 5 π‘₯ = 7 2 , giving values to three decimal places.

  • A { 0 . 7 2 7 , βˆ’ 1 . 9 2 7 }
  • B { 5 . 2 2 2 , βˆ’ 4 . 0 2 2 }
  • C { 1 . 9 2 7 , βˆ’ 0 . 7 2 7 }
  • D { 4 . 0 2 2 , βˆ’ 5 . 2 2 2 }