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KVPY2017MathematicsSequences and Series

Let x₁, x₂, , x₆ be the roots of the polynomial equation x ⁶+2 x ⁵+4 x ⁴+8 x ³+16 x ²+32 x +64=0 Then

Options

  1. A| x _ i |=2 for exactly one value of i
  2. B|x_ i |=2 for exactly two values of i
  3. C| x _ i |=2 for all values of i
  4. D| x _ i |=2 for no value of i

Correct answer

C. | x _ i |=2 for all values of i

Step-by-step solution

It form an G.P. x⁶ (1- ( 2 x )⁷ ) (1- 2 x ) =0 solve that array l x⁷=2⁷ x=2 array

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