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Home Aptitude Quadratic Equation See What Others Are Saying!
  • Question
  • Two students A and B solve an equation of the from x 2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. B starts with a wrong value of q and gets the roots as 2 and -9. What are the correct roots of the equation?


  • Options
  • A. 3 and - 4
  • B. - 3 and - 4
  • C. - 3 and 4
  • D. 3 and 4

  • Correct Answer
  • - 3 and - 4 

    Explanation

    Let ? and ? be the roots of the quadratic equation x2 + px + q = 0
    Given that, A starts with a wrong value of p and obtains the roots as 2 and 6. But this time q is correct. i.e products of roots
    = q = ? . ? = 6 x 2 = 12 ...(i)
    and B starts with a wrong value of q and gets the roots as 2 and - 9. But this time p is correct i.e., sum of roots
    = p = ? + ? = - 9 + 2 = - 7 ..(ii)
    (? - ?)2 = (? + ?)2 - 4? ?
    = (-7)2 - 4.12 = 49 - 48 = 1
    [from Eqs. (i) and (ii)]
    ? ? - ? = 1 ..(iii)
    Now, from Eqs. (ii) and (iii) , we get
    ? = - 3 and ? = - 4
    which are correct roots .


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