If the roots of the equation 1x+p+1x+q=1rare equal in magnitude but opposite in sign, then the product of the roots will be

If the roots of the equation 1x+p+1x+q=1rare equal in magnitude but opposite in sign, then the product of the roots will be

  1. A

    p2+q22

  2. B

    p2+q22

  3. C

    p2q22

  4. D

    p2q22

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    Solution:

    Given equation 1x+p+1x+q=1rcan be rewritten as
    x2+x(p+q2r)+pqprqr=0……………………….(i)
    Let roots are α and - α, then the product of roots
    α2=pqprqr=pqr(p+q)………………………(ii)
    and            sum of roots, 0=(p+q2r)
                              r=p+q2……………………….(iii)
    On solving Eqs. (ii) and (iii), we get
    α2=pqp+q2(p+q)=12(p+q)22pq α2=p2+q22

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