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AP EAMCET202319 May 2023Morning ShiftMathematicsQuadratic EquationActual

If the roots of the equation 6 x^3-11 x^2+6 x-1=0 are in harmonic progression, then the roots of x^3-6 x^2+11 x-6=0 will be in

Options

  1. AGeometric Progression
  2. BArithmetic Progression
  3. CHarmonic Progression
  4. DArithmetico-Geometric Progression

Correct answer

B. Arithmetic Progression

Step-by-step solution

Consider x^3-6 x^2+11 x-6=0 ...(i) Since x=1 , satisfies the above equation. Hence (x-1) will be a factor of equation (i) Therefore aligned & x^2(x-1)-5 x(x-1)+6(x-1)=0 & (x^2-5 x+6 )(x-1)=0 & (x-3)(x-2)(x-1)=0 x=1,2,3 aligned Since 2-1=1=3-2 Hence roots of equation is in Arithmetic progression.

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