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For the equation 2( x- 2 x)- 2 x(1+2 x)+2 x=0, x [0,2 ]-

Options

  1. Athe values of x satisfying the given equation forms an A.P.
  2. Bthe sum of all possible values of x satisfying the given equation is 4
  3. Cthe sum of all possible values of x in [0,2 ] satisfying the given equation is 9 2
  4. Dthere are five solutions of the equation in [0,2 ]

Correct answer

D. there are five solutions of the equation in [0,2 ]

Step-by-step solution

aligned & 2 x-2 2 x- 2 x-2 x 2 x+2 x=0 & 2 x-2 x- 2 x- x+ 3 x+2 x=0 & 2 x(1- x)+4 ^3 x-3 x & -2 (2 ^2 x-1 )+ x=0 & 2 x(1- x)+4 ^3 x-4 ^2 x-2 x+2=0 & 2 x(1- x)+4 ^2 x( x-1)-2( x-1)=0 & (1- x) 2 x+2-4 (1- ^2 x ) =0 & (1- x) 4 ^2 x+2 x-2 =0 & (1- x)( x+1)(2 x-1)=0 & x=0,2 , 3 2 , 6 , 5 6 aligned

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