If f(x)=(x−2)(x−3)(x−4)(x−5)(x−6) then 

If f(x)=(x2)(x3)(x4)(x5)(x6) then 

  1. A

    f(x)=0has five real roots

  2. B

    four roots of  f(x)=0 lie in  (2,3)(3,4)(4,5)(5,6)

  3. C

    the equation f(x) has only three roots.

  4. D

    four roots of f(x) = 0 lie in (1,2)(2,3)(3,4)(4,5)

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    Solution:

    If f(x)=(x2)(x3)(x4)(x5)(x6)

    so, by Rolle's theorem applied on [2, 3], [3, 4], [4,

    5], [5, 6] there are x1(2,3),x2(3,4),x3(4

     5), x4(5,6) such that  fxi=0,i=1,2,3,4

    Since f' is polynomial of degree 4 so cannot have five roots

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