The harmonic mean of the roots of the equation (5+2)x2−(4+5)x+8+25=0 is

The harmonic mean of the roots of the equation (5+2)x2(4+5)x+8+25=0 is

  1. A

    2

  2. B

    4

  3. C

    6

  4. D

    8

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    Solution:

     Given equation is  (5+2)x2(4+5)x+8+25=0
    Let x1 and x2 are the roots of the equation
                     x1+x2=4+55+2………………….(i)
    and x1x2=8+255+2=2(4+5)5+2=2x1+x2…(ii)
      Harmonic mean =2x1x2x1+x2=4x1+x2x1+x2=4
                                                                      [ from Eq. (ii)]

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