Lesson Worksheet: Solving Quadratic Equations: Quadratic Formula Mathematics • 9th Grade

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 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}

Q3:

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}

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 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}

Q6:

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}

Q7:

A student correctly substitutes values into a quadratic formula as follows: 𝑥=5±25808. What is the quadratic equation they were trying to solve?

  • A8𝑥5𝑥52=0
  • B4𝑥+5𝑥5=0
  • C4𝑥5𝑥+5=0
  • D8𝑥+5𝑥52=0
  • E4𝑥+5𝑥+5=0

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:

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

Q10:

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

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