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 βˆ’π‘₯+7π‘₯+1=0.

  • A7βˆ’βˆš532,7+√532
  • B7βˆ’βˆš512,7+√512
  • C49βˆ’βˆš112,49+√112
  • D7βˆ’βˆš112,7+√112

Q2:

Find the solution set of the equation 6π‘₯βˆ’8π‘₯+1=0, giving values to two decimal places.

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

Q3:

Find the solution set of π‘₯βˆ’6(π‘₯βˆ’1)=2 in ℝ, giving values to two decimal places.

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

Q4:

Find the solution set of the equation 5π‘₯(π‘₯βˆ’6)βˆ’3(π‘₯+4)+3=0, giving values to one decimal place.

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

Q5:

Find the solution set of the equation (π‘₯βˆ’23)βˆ’6π‘₯=0, giving values to three decimal places.

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

Q6:

Find the solution set of the equationβˆ’5βˆ’5π‘₯=1π‘₯ in ℝ, giving values to one decimal place.

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

Q7:

A student correctly substitutes values into a quadratic formula as follows: π‘₯=5±√25βˆ’808. What is the quadratic equation they were trying to solve?

  • A8π‘₯βˆ’5π‘₯βˆ’52=0
  • B4π‘₯+5π‘₯βˆ’5=0
  • C4π‘₯βˆ’5π‘₯+5=0
  • D8π‘₯+5π‘₯βˆ’52=0
  • E4π‘₯+5π‘₯+5=0

Q8:

Given that π‘₯=βˆ’2 is a root of the equation π‘₯βˆ’4π‘šπ‘₯βˆ’ο€Ήπ‘šβˆ’6=0, find the set of possible values of π‘š.

  • A4βˆ’2√3,4+2√3
  • B32βˆ’2√3,32+2√3
  • Cο―βˆ’8+2√2620,βˆ’8βˆ’2√2620
  • D4βˆ’βˆš26,4+√26
  • E8βˆ’βˆš6640,8+√6640

Q9:

Using the quadratic formula, find all the solutions to π‘₯βˆ’10π‘₯+1=0οŠͺ.

  • Aπ‘₯=5+√15, π‘₯=βˆ’ο„5+√15, π‘₯=5βˆ’2√15, π‘₯=βˆ’ο„5βˆ’βˆš15
  • Bπ‘₯=5+√34, π‘₯=βˆ’ο„5+√34, π‘₯=5βˆ’2√34, π‘₯=βˆ’ο„5βˆ’βˆš34
  • Cπ‘₯=5+2√6, π‘₯=5βˆ’2√6
  • Dπ‘₯=5+2√6, π‘₯=βˆ’ο„5+2√6, π‘₯=5βˆ’2√6, π‘₯=βˆ’ο„5βˆ’2√6
  • Eπ‘₯=5+√15, π‘₯=5βˆ’βˆš15

Q10:

Use the quadratic formula to find all the values of π‘Ž for which the roots of the equation 2π‘₯+π‘Žπ‘₯βˆ’7=0 differ by exactly 10. Give your answers correct to two decimal places if necessary.

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

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