Worksheet: Solving Quadratic Equations: Quadratic Formula

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

Q1:

Solve the equation βˆ’π‘₯+7π‘₯+1=0.

  • Aο―βˆ’7+√532,βˆ’7βˆ’βˆš532
  • B7βˆ’βˆš532,7+√532
  • C7βˆ’βˆš512,7+√512
  • D49βˆ’βˆš112,49+√112
  • E7βˆ’βˆš112,7+√112

Q2:

Find the solution set of the equation 3π‘₯βˆ’2(7βˆ’π‘₯)=0, giving values to one decimal place.

  • A{1.9,βˆ’2.5}
  • B{βˆ’1.9,βˆ’2.5}
  • C{3.7,βˆ’5.0}
  • D{βˆ’3.7,βˆ’5.0}

Q3:

Find the solution set of the equation π‘₯βˆ’8π‘₯βˆ’2=9π‘₯+8, giving values correct to three decimal places.

  • A{17.569,βˆ’0.569}
  • B{0.569,βˆ’17.569}
  • C{8.785,βˆ’0.285}
  • D{0.285,βˆ’8.785}

Q4:

Find the solution set of the equation 5π‘₯βˆ’7π‘₯βˆ’32=0, giving values to three decimal places.

  • A{6.650,βˆ’3.850}
  • B{βˆ’3.325,1.925}
  • C{βˆ’6.650,βˆ’3.850}
  • D{3.325,βˆ’3.850}
  • E{3.325,βˆ’1.925}

Q5:

Find the solution set of the equation 18π‘₯+5π‘₯=1, giving values to three decimal places.

  • A{7.424,βˆ’2.424}
  • B{βˆ’7.424,4.849}
  • C{βˆ’14.849,4.849}
  • D{βˆ’7.424,2.424}

Q6:

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}

Q7:

Find the solution set of the equation 2π‘₯βˆ’5=6π‘₯, giving values to three decimal places.

  • A{1.772,βˆ’6.772}
  • B{0.886,βˆ’3.386}
  • C{6.772,βˆ’1.772}
  • D{3.386,βˆ’0.886}

Q8:

The sum of the roots of the equation 4π‘₯+π‘˜π‘₯βˆ’4=0 is βˆ’1. Find the value of π‘˜ and the solution set of the equation.

  • A4, ο―βˆ’1βˆ’βˆš22,βˆ’1+√22
  • Bβˆ’4, 1βˆ’βˆš52,1+√52
  • Cβˆ’4, 1+√22,1βˆ’βˆš22
  • D4, ο―βˆ’1βˆ’βˆš52,βˆ’1+√52

Q9:

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

Q10:

Find the solution set of the equation 3π‘₯+3βˆ’4π‘₯βˆ’3=3 in ℝ, giving values to one decimal place.

  • A{1.3,βˆ’1.6}
  • B{1.4,βˆ’1.4}
  • C{1.6,βˆ’1.3}
  • D{7.5,βˆ’9.5}

Q11:

Find the solution set of the equation βˆ’3π‘₯βˆ’π‘₯+12=0 in ℝ, giving values to one decimal place.

  • A{11.0,βˆ’13.0}
  • B{βˆ’1.8,2.2}
  • C{βˆ’2.2,1.8}
  • D{βˆ’2.0,2.0}

Q12:

Find the solution set of π‘₯+17π‘₯=6 in ℝ, giving values to one decimal place.

  • A{βˆ’0.2,0.2}
  • B{βˆ’0.3,0.3}
  • C{5.8,βˆ’5.8}
  • Dβˆ…

Q13:

By using the quadratic formula, solve the equation 2π‘₯+3π‘₯=7. Give your answers correct to two decimal places.

  • Aπ‘₯=76, π‘₯=βˆ’76
  • Bπ‘₯=1.54, π‘₯=βˆ’4.544
  • Cπ‘₯=βˆ’0.75+1.71𝑖, π‘₯=βˆ’0.75βˆ’1.71𝑖
  • Dπ‘₯=βˆ’2.77, π‘₯=1.27
  • Eπ‘₯=1.27

Q14:

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

Q15:

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}

Q16:

Find the solution set in ℝ of the equation 4π‘₯βˆ’2π‘₯=1, giving values to one decimal place.

  • A{0.6,βˆ’0.8}
  • B{6.7,βˆ’4.7}
  • C{0.8,βˆ’0.6}
  • D{4.7,βˆ’6.7}

Q17:

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

Q18:

Find the solution set of the equation π‘₯+46π‘₯=22, giving values to three decimal places.

  • A{19.660,4.679}
  • B{βˆ’39.321,4.679}
  • C{βˆ’19.660,2.340}
  • D{19.660,2.340}
  • E{39.321,4.679}

Q19:

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}

Q20:

Find the solution set of the equation π‘₯(π‘₯βˆ’36)=21, giving values to three decimal places.

  • A{36.574,βˆ’0.574}
  • B{36.574,βˆ’1.148}
  • C{73.148,βˆ’1.148}
  • D{βˆ’36.574,0.574}
  • E{βˆ’73.148,βˆ’1.148}

Q21:

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}

Q22:

Find the solution set of the equation π‘₯=βˆ’18π‘₯+6, giving values to three decimal places.

  • A{18.327,βˆ’0.327}
  • B{0.327,βˆ’18.327}
  • C{0.164,βˆ’9.164}
  • D{9.164,βˆ’0.164}

Q23:

Find the solution set of the equation 9π‘₯βˆ’4π‘₯=20, giving values to three decimal places.

  • A{3.459,βˆ’2.570}
  • B{1.729,βˆ’1.285}
  • C{2.570,βˆ’3.459}
  • D{1.285,βˆ’1.729}

Q24:

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}

Q25:

Find the solution set of the equation βˆ’π‘₯βˆ’1βˆ’2π‘₯βˆ’6=15 in ℝ, giving values to one decimal place.

  • A{6.9,βˆ’2.9}
  • B{βˆ’0.7,0.3}
  • C{βˆ’0.3,0.7}
  • D{βˆ’0.0,1.0}

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