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Home ‣ Aptitude ‣ Quadratic Equation See What Others Are Saying!
  • Question

  • If ? and ? be the roots of the equation ax 2 + bx + c = 0, find the value of ? 2/? + ? 2/? .


  • Options
  • A. ab -b2c/2b2c
  • B. 3bc - a3/b2c
  • C. 3ac - b2/a3c
  • D. 3abc - b3/a2c

  • Correct Answer
  • 3abc - b3/a2c 

    Explanation

    Given, ? and ? are the roots of the equation ax2 + bx + c = 0
    ? Sum of two roots = -b/a
    ? + ? = -b/a
    and product of two roots = c/a
    ? ? = c/a
    ? ?2/? + ?2/? = ( ?3 + ?3) / ? ?
    = [(? + ?) 3 - 3 ? ? (? + ?)] / ??
    [? (a + b)3 = a3 + b3 + 3ab(a + b) ]
    = (-b/a)3 - [3c/a(-b/a)/c/a = -b3/a3 + 3bc/a2]/(c/a)
    = 3abc - b3/a2c

    • More questions

    • 1. 
      Shankara buys a watch for Rs. 1,950 in cash and sells it for Rs. 2,200 at a credit of 1 year. If the rate of interest is 10% per annum, he _____ :

    • Options
    • A. gains Rs. 55
    • B. gains Rs. 50
    • C. loses Rs. 30
    • D. gains Rs. 30
      • Discuss
    • 2. 
      ABCD is a rhombus with ? ABC = 56°, then ? ACD is equal to :

    • Options
    • A. 90°
    • B. 60°
    • C. 56°
    • D. 62°
      • Discuss
    • 3. 
      The shaded region represents

    • Options
    • A. y ? x
    • B. y ? ? x
    • C. y ? x
    • D. y ? ? x
      • Discuss
    • 4. 
      45 x? = 25% of 900

    • Options
    • A. 16.20
    • B. 4
    • C. 5
    • D. 500
      • Discuss
    • 5. 
      Rajan sold an articles for ? 6000 at a loss of 25%. Find the cost price.?

    • Options
    • A. ? 7500
    • B. ? 7200
    • C. ? 8000
    • D. ? 8500
      • Discuss
    • 6. 
      In which of the following cases, A = B?

    • Options
    • A. A = {12, 14, 16}, B = {16, 18, 20}
    • B. A = ?, b = {}
    • C. A = {x: x ? W and x < 1}, B = ?
    • D. A = {x: x is a day of the week beginning with S}, B = {Sunday}
      • Discuss
    • 7. 10, 25, 45, 54, 60, 75, 80

    • Options
    • A. 10
    • B. 45
    • C. 54
    • D. 75
      • Discuss
    • 8. 
      If two parallel lines are intersected by a transversal, then the bisectors of the two pairs of interior angles enclose a:

    • Options
    • A. Trapezium
    • B. Rectangle
    • C. Square
    • D. circle
      • Discuss
    • 9. 
      ?. 6x 2 + 77x + 121 = 0
      ?. y 2 + 9y ? 22 = 0

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
      • Discuss
    • 10. 
      The length of minute hand of a wall clock is 7 cms. The area swept by minute hand in 30 minutes is?

    • Options
    • A. 147 sq. cm
    • B. 210 sq. cm
    • C. 154 sq. cm
    • D. 77 sq. cm
      • Discuss

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