Lesson Worksheet: Quadratic Equations: 𝑥² + 𝑏𝑥 + 𝑐 = 0 Mathematics

In this worksheet, we will practice factoring trinomials and solving quadratic equations whose form is 𝑥² + 𝑏𝑥 + 𝑐 = 0.


Identify the solutions to the equation 𝑥(𝑥1)=0.

  • A𝑥=0, 𝑥=1
  • B𝑥=1, 𝑥=1
  • C𝑥=0
  • D𝑥=0, 𝑥=1
  • E𝑥=1


Solve the equation 𝑥2𝑥=𝑥2 by factoring.

  • A𝑥=1 or 𝑥=2
  • B𝑥=1 or 𝑥=2
  • C𝑥=1 or 𝑥=2
  • D𝑥=1 or 𝑥=4
  • E𝑥=4 or 𝑥=1


Given that a root of the equation 𝑥+18𝑥+𝑘=0 is 𝑥=3, what is the value of 𝑘?


Given that 𝑥=𝑎+3 is a solution of the equation (𝑥+𝑎)(𝑥𝑎)=𝑥𝑎𝑥+21, find the value of 𝑎.


Solve 𝑥+2𝑥3=0.

  • A𝑥=1 or 𝑥=3
  • B𝑥=1
  • C𝑥=1 or 𝑥=3
  • D𝑥=1 or 𝑥=3
  • E𝑥=3


Solve the equation 𝑥8𝑥+16=0 by factoring.

  • A𝑥=4
  • B𝑥=4
  • C𝑥=8 or 𝑥=2
  • D𝑥=8 or 𝑥=2


Find the solution set of the equation 𝑥+2𝑥=0 in .

  • A{2,0}
  • B{0}
  • C{2}
  • D{(2,0)}
  • E{2,0}


Find the solution set of 𝑥+5𝑥36=0 in .

  • A{4,9}
  • B{2,18}
  • C{4,9}
  • D{2,18}
  • E{1,36}


Find the solution set of 𝑥(𝑥19)=15𝑥 in .

  • A{4}
  • B{0,4}
  • C{4}
  • D{19,15}
  • E{0,4}


Find the solution set of (𝑥+2)(𝑥7)=8 in .

  • A{2,7}
  • B{1,6}
  • C{2,3}
  • D{2,3}
  • E{1,6}

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