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AP EAMCET202022 Sep 2020Evening ShiftMathematicsQuadratic EquationActual

If the roots of x^3-p x^2+q x-r=0 are in AP. Then,

Options

  1. A2 p^3-9 p q+27 r=0
  2. B2 p^3+9 p q-27 r=0
  3. C2 p^3-8 p q+27 r=0
  4. D2 p^3-9 p q+28 r=0

Correct answer

A. 2 p^3-9 p q+27 r=0

Step-by-step solution

Let a-d, a, a+d are roots of x^3-p x^2+q x-r=0 Sum of roots =- b a aligned a-d+a+a+d & =- (-p) 1 3 a & =p a & = p 3 aligned Since, a= P 3 should be satisfied by given equation. So, put x= p 3 in Eq. (i) ( p 3 )^3-P ( p 3 )^2+q ( p 3 )-r=0 aligned p^3 27 - p^3 9 + p q 3 -r & =0 p^3-3 p^3+9 p q-27 r & =0 -2 p^3+9 p q-27 r & =0 2 p^3-9 p q+27 r & =0 aligned Hence, option (1) is correct.

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