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AP EAMCET2013MathematicsQuadratic Equation

If the roots of x^3-42 x^2+336 x-512=0 , are in increasing geometric progression, then its common ratio is

Options

  1. A2: 1
  2. B3: 1
  3. C4: 1
  4. D6: 1

Correct answer

C. 4: 1

Step-by-step solution

Given, cubic equation is aligned & x^3-42 x^2+336 x-512=0 & x^2(x-2)-40 x(x-2)+256(x-2)=0 & (x-2) (x^2-40 x+256 )=0 & aligned array rlrl & (x-2) x^2-32 x-8 x+256 & =0 & & (x-2) x(x-32)-8(x-32) & =0 & & (x-2)(x-32)(x-8) & =0 & & (x-2)(x-8)(x-32) & =0 & & x=2,8,32 array Which represents a geometric progression in increasing order. Common ratio = 8 2 =4: 1

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