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

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

Q1:

Identify the solutions to the equation 𝑥(𝑥−1)=0.

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

Q2:

Solve the equation 𝑥−2𝑥=𝑥−2 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

Q3:

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

Q4:

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

Q5:

Solve 𝑥+2𝑥−3=0.

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

Q6:

Solve the equation 𝑥−8𝑥+16=0 by factoring.

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

Q7:

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

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

Q8:

Find the solution set of 𝑥+5𝑥−36=0 in ℝ.

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

Q9:

Find the solution set of 𝑥(𝑥−19)=−15𝑥 in ℝ.

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

Q10:

Find the solution set of (𝑥+2)(𝑥−7)=−8 in ℝ.

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

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