Lesson Worksheet: Solving Quadratic Equations: Quadratic Formula Mathematics

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

Q1:

Find the solution set of the equation 𝑥3𝑥+1=0, giving values correct to two decimal places.

  • A{2.62,0.38}
  • B{5.24,0.76}
  • C{3.12,0.12}
  • D{2.62,0.38}
  • E{5.24,0.76}

Q2:

Solve the equation 𝑥+7𝑥+1=0.

  • A7+532,7532
  • B7532,7+532
  • C7512,7+512
  • D49112,49+112
  • E7112,7+112

Q3:

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}

Q4:

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}

Q5:

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

Q6:

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}

Q7:

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}

Q8:

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

Q9:

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

Q10:

A stone is thrown upward from the top of a cliff and lands in the sea some time later. The height, , above sea level at any time, 𝑡 seconds, is given by the formula =3𝑡5𝑡+40.

After how many seconds will the stone reach the sea? Give your answer to the nearest tenth of a second.

This lesson includes 24 additional questions and 269 additional question variations for subscribers.

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