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.

  • A7532,7+532
  • B7512,7+512
  • C49112,49+112
  • D7112,7+112

Q2:

Find the solution set of the equation 3𝑥2(7𝑥)=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 𝑥8𝑥2=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 5𝑥7𝑥32=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(𝑥6)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 2𝑥5=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+𝑘𝑥4=0 is 1. Find the value of 𝑘 and the solution set of the equation.

  • A4, 122,1+22
  • B4, 152,1+52
  • C4, 1+22,122
  • D4, 152,1+52

Q9:

Given that 𝑥=2 is a root of the equation 𝑥4𝑚𝑥𝑚6=0, find the set of possible values of 𝑚.

  • A423,4+23
  • B3223,32+23
  • C8+22620,822620
  • D426,4+26
  • E86640,8+6640

Q10:

Find the solution set of the equation 3𝑥+34𝑥3=3 in , 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 3𝑥𝑥+12=0 in , 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 , 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=0.751.71𝑖
  • 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+𝑎𝑥7=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 (𝑥23)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 of the equation 4𝑥2𝑥=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 𝑥10𝑥+1=0.

  • A𝑥=5+15, 𝑥=5+15, 𝑥=5215, 𝑥=515
  • B𝑥=5+34, 𝑥=5+34, 𝑥=5234, 𝑥=534
  • C𝑥=5+26, 𝑥=526
  • D𝑥=5+26, 𝑥=5+26, 𝑥=526, 𝑥=526
  • E𝑥=5+15, 𝑥=515

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 𝑥6(𝑥1)=2 in , 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(𝑥36)=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 6𝑥8𝑥+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 9𝑥4𝑥=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 equation55𝑥=1𝑥 in , 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 𝑥12𝑥6=15 in , 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.