Lesson Worksheet: Solving Quadratic Equations: Quadratic Formula Mathematics

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

Q1:

Solve the equation −𝑥+7𝑥+1=0.

  • A7−√532,7+√532
  • B7−√512,7+√512
  • C49−√112,49+√112
  • D7−√112,7+√112

Q2:

Find the solution set of the equation 3𝑥−2(7−𝑥)=0, giving values to one decimal place.

  • A{1.9,−2.5}
  • B{−1.9,−2.5}
  • C{3.7,−5.0}
  • D{−3.7,−5.0}

Q3:

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}

Q4:

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}

Q5:

Find the solution set of the equation 18𝑥+5𝑥=1, giving values to three decimal places.

  • A{7.424,−2.424}
  • B{−7.424,4.849}
  • C{−14.849,4.849}
  • D{−7.424,2.424}

Q6:

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}

Q7:

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}

Q8:

The sum of the roots of the equation 4𝑥+𝑘𝑥−4=0 is −1. Find the value of 𝑘 and the solution set of the equation.

  • A4, −1−√22,−1+√22
  • B−4, 1−√52,1+√52
  • C−4, 1+√22,1−√22
  • D4, −1−√52,−1+√52

Q9:

Given that 𝑥=−2 is a root of the equation 𝑥−4𝑚𝑥−𝑚−6=0, find the set of possible values of 𝑚.

  • A4−2√3,4+2√3
  • B32−2√3,32+2√3
  • C−8+2√2620,−8−2√2620
  • D4−√26,4+√26
  • E8−√6640,8+√6640

Q10:

Find the solution set of the equation 3𝑥+3−4𝑥−3=3 in ℝ, giving values to one decimal place.

  • A{1.3,−1.6}
  • B{1.4,−1.4}
  • C{1.6,−1.3}
  • D{7.5,−9.5}

Q11:

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}

Q12:

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∅

Q13:

By using the quadratic formula, solve the equation 2𝑥+3𝑥=7. Give your answers correct to two decimal places.

  • A𝑥=76, 𝑥=−76
  • B𝑥=1.54, 𝑥=−4.544
  • C𝑥=−0.75+1.71𝑖, 𝑥=−0.75−1.71𝑖
  • D𝑥=−2.77, 𝑥=1.27
  • E𝑥=1.27

Q14:

Use the quadratic formula to find all the values of 𝑎 for which the roots of the equation 2𝑥+𝑎𝑥−7=0 differ by exactly 10. Give your answers correct to two decimal places if necessary.

  • A20, −20
  • B9.27, −9.27
  • C4, −4
  • D9.79, −9.79
  • E18.55, −18.55

Q15:

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}

Q16:

Find the solution set in ℝ of the equation 4𝑥−2𝑥=1, giving values to one decimal place.

  • A{0.6,−0.8}
  • B{6.7,−4.7}
  • C{0.8,−0.6}
  • D{4.7,−6.7}

Q17:

Using the quadratic formula, find all the solutions to 𝑥−10𝑥+1=0.

  • A𝑥=5+√15, 𝑥=−5+√15, 𝑥=5−2√15, 𝑥=−5−√15
  • B𝑥=5+√34, 𝑥=−5+√34, 𝑥=5−2√34, 𝑥=−5−√34
  • C𝑥=5+2√6, 𝑥=5−2√6
  • D𝑥=5+2√6, 𝑥=−5+2√6, 𝑥=5−2√6, 𝑥=−5−2√6
  • E𝑥=5+√15, 𝑥=5−√15

Q18:

Find the solution set of the equation 𝑥+46𝑥=22, giving values to three decimal places.

  • A{19.660,4.679}
  • B{−39.321,4.679}
  • C{−19.660,2.340}
  • D{19.660,2.340}
  • E{39.321,4.679}

Q19:

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}

Q20:

Find the solution set of the equation 𝑥(𝑥−36)=21, giving values to three decimal places.

  • A{36.574,−0.574}
  • B{36.574,−1.148}
  • C{73.148,−1.148}
  • D{−36.574,0.574}
  • E{−73.148,−1.148}

Q21:

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}

Q22:

Find the solution set of the equation 𝑥=−18𝑥+6, giving values to three decimal places.

  • A{18.327,−0.327}
  • B{0.327,−18.327}
  • C{0.164,−9.164}
  • D{9.164,−0.164}

Q23:

Find the solution set of the equation 9𝑥−4𝑥=20, giving values to three decimal places.

  • A{3.459,−2.570}
  • B{1.729,−1.285}
  • C{2.570,−3.459}
  • D{1.285,−1.729}

Q24:

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}

Q25:

Find the solution set of the equation −𝑥−1−2𝑥−6=15 in ℝ, giving values to one decimal place.

  • A{6.9,−2.9}
  • B{−0.7,0.3}
  • C{−0.3,0.7}
  • D{−0.0,1.0}

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.