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

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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 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}

Q3:

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}

Q4:

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}

Q5:

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}

Q6:

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}

Q7:

A student correctly substitutes values into a quadratic formula as follows: 𝑥=5±√25−808. What is the quadratic equation they were trying to solve?

  • A8𝑥−5𝑥−52=0
  • B4𝑥+5𝑥−5=0
  • C4𝑥−5𝑥+5=0
  • D8𝑥+5𝑥−52=0
  • E4𝑥+5𝑥+5=0

Q8:

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

Q9:

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

Q10:

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

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