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AP EAMCET2009MathematicsQuadratic Equation

If and are the roots of x^2-2 x+4=0 , then the value of ^6+ ^6 is

Options

  1. A32
  2. B64
  3. C128
  4. D256

Correct answer

C. 128

Step-by-step solution

Given, , are the roots of x^2-2 x+4=0 Now, aligned - & = ( + )^2-4 & = 4-4 4 = -12 aligned On solving Eqs. (i) and (ii), we get = 2+2 3 i 2 =-2 ( -1- 3 i 2 )=-2 ^2 and = 2-2 3 i 2 =-2 ( -1+ 3 i 2 )=-2 Now, aligned ^6+ ^6 & = (-2 ^2 )^6+(-2 )^6 & =64 ( ^3 )^4+64 ( ^3 )^2 & =128 [ ^3=1 ] aligned

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