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AP EAMCET202421 May 2024Evening ShiftMathematicsQuadratic EquationActual

The condition that the roots of x^3-b x^2+c x-d=0 are in arithmetic progression is

Options

  1. A9 c b=2 b^3+27 d
  2. B9 c b=2 d^3+27 b
  3. C9 c d=2 d^3+27 b
  4. D9 c d=2 b^3+27 d

Correct answer

A. 9 c b=2 b^3+27 d

Step-by-step solution

Let roots in A.P. be as -r, , +r Sum of roots =b -r+ + +r=b = b 3 is root of x^3-b x^2+c x-d=0 b^3 27 - b^3 9 + b c 3 -d=0 9 c b=2 b^3+27 d

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