Lesson Worksheet: Solving Quadratic Equations by Using the Quadratic Formula Mathematics

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In this worksheet, we will practice solving quadratic equations by using the quadratic formula.

Q1:

Find the solution set of the equation 6𝑥−8𝑥+1=0, giving values to two decimal places.

  • A{−2.39,−0.28}
  • B{2.39,0.28}
  • C{−1.19,−0.14}
  • D{1.19,0.14}

Q2:

Find the solution set of 𝑥−6(𝑥−1)=2 in ℝ, giving values to two decimal places.

  • A{6.61,−0.61}
  • B{−10.47,−1.53}
  • C{5.24,0.76}
  • D{10.47,1.53}
  • E{−5.24,−0.76}

Q3:

Find the solution set of the equation 5𝑥−7𝑥−32=0, giving values to three decimal places.

  • A{6.650,−3.850}
  • B{−3.325,1.925}
  • C{−6.650,−3.850}
  • D{3.325,−3.850}
  • E{3.325,−1.925}

Q4:

Find the solution set of the equation 5𝑥(𝑥−6)−3(𝑥+4)+3=0, giving values to one decimal place.

  • A{−13.7,−0.5}
  • B{6.9,−0.3}
  • C{13.7,−0.5}
  • D{−6.9,−0.3}

Q5:

Find the solution set of the equation (𝑥−23)−6𝑥=0, giving values to three decimal places.

  • A{38.124,27.751}
  • B{76.249,27.751}
  • C{−38.124,13.876}
  • D{−76.249,27.751}
  • E{38.124,13.876}

Q6:

Find the solution set of the equation−5−5𝑥=1𝑥 in ℝ, giving values to one decimal place.

  • A{−0.7,−0.3}
  • B{−1.0,0.0}
  • C{0.3,0.7}
  • D{−2.8,−7.2}

Q7:

Find the solution set of the equation 𝑥−8𝑥−2=9𝑥+8, giving values correct to three decimal places.

  • A{17.569,−0.569}
  • B{0.569,−17.569}
  • C{8.785,−0.285}
  • D{0.285,−8.785}

Q8:

Find the solution set of the equation 2𝑥−5=6𝑥, giving values to three decimal places.

  • A{1.772,−6.772}
  • B{0.886,−3.386}
  • C{6.772,−1.772}
  • D{3.386,−0.886}

Q9:

Find the solution set of the equation −3𝑥−𝑥+12=0 in ℝ, giving values to one decimal place.

  • A{11.0,−13.0}
  • B{−1.8,2.2}
  • C{−2.2,1.8}
  • D{−2.0,2.0}

Q10:

Find the solution set of 𝑥+17𝑥=6 in ℝ, giving values to one decimal place.

  • A{−0.2,0.2}
  • B{−0.3,0.3}
  • C{5.8,−5.8}
  • D∅

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