Let $p, q$ and $r$  be real numbers $(p \ne q,r \ne 0),$ such that the roots of the equation $\frac{1}{{x + p}} + \frac{1}{{x + q}} = \frac{1}{r}$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to .

  • [JEE MAIN 2018]
  • A

    ${p^2} + {q^2} + {r^2}$

  • B

    ${p^2} + {q^2}$

  • C

    $2({p^2} + {q^2})$

  • D

    $\frac{{{p^2} + {q^2}}}{2}$

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