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Home Aptitude Quadratic Equation See What Others Are Saying!
  • Question
  • If one of the roots of the equation x 2 - bx + c = 0 is the square of the other, then which of the following option is correct?


  • Options
  • A. b3 = 3bc + c2 + c
  • B. c3 = 3bc + b2 + b
  • C. 3bc = c3 + b2 + b
  • D. 3bc = c3 + b3 + b2

  • Correct Answer
  • b3 = 3bc + c2 + c 

    Explanation

    Given that, one root of the equation
    x2 - bx + c = 0 is square of other root of this equation i.e., roots (?, ?2).
    ? Sum of roots = ? + ?2 = -(-b)/1
    ? ? (? + 1) = b .......(i)
    and product of roots= ?. ?2 = c/1
    ? ?3 = c ? = c1/3 ....(ii)
    From Eqs. (i) and (ii).
    c1/3 (c1/3 + 1) = b ....(iii)
    On cubing both sides, we get
    c(c1/3 + 1)3 = b3
    ? c {c + 1 + 3c1/3 (c1/3 + 1)} = b3
    ? c {c + 1 = 3b} = b3 [from Eq. (iii)]
    ? b3 = 3bc + c2 + c


  • More questions

    • 1. 
      A train 300 meters long passes a standing man is 15 seconds. The speed of the train is?

    • Options
    • A. 40 km/hr
    • B. 50 km/hr
    • C. 60 km/hr
    • D. 72 km/hr
    • Discuss
    • 2. 
      If the diagonal of a square is double, how does the area of the square change?

    • Options
    • A. Becomes four fold
    • B. Becomes three fold
    • C. Becomes two fold
    • D. None of the above
    • Discuss
    • 3. 46080, 3840, 384, 48, 24, 2, 1

    • Options
    • A. 1
    • B. 2
    • C. 24
    • D. 384
    • Discuss
    • 4. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

    • Options
    • A. 1520 m2
    • B. 2420 m2
    • C. 2480 m2
    • D. 2520 m2
    • Discuss
    • 5. 
      4/5 of a number exceeds its 2/3 by 8. The number is?

    • Options
    • A. 30
    • B. 60
    • C. 90
    • D. None of these
    • Discuss
    • 6. 
      Find the angle between minute hand and hour hand at 2 : 18 AM

    • Options
    • A. 37°
    • B. 33°
    • C. 39°
    • D. None of these
    • Discuss
    • 7. 
      Rakesh, Dinesh and Mahesh start a business by investing ? 5000 , ? 8000 and ? 12000 , respectively . At the end of year, they got the profit of ? 12500. What is the share of Dinesh in profit?

    • Options
    • A. ? 4000
    • B. ? 4500
    • C. ? 6000
    • D. ? 7500
    • Discuss
    • 8. The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

    • Options
    • A. 74
    • B. 94
    • C. 184
    • D. 364
    • Discuss
    • 9. If log 27 = 1.431, then the value of log 9 is:

    • Options
    • A. 0.934
    • B. 0.945
    • C. 0.954
    • D. 0.958
    • Discuss
    • 10. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

    • Options
    • A. 32
    • B. 48
    • C. 64
    • D. 96
    • E. None of these
    • Discuss


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