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AP EAMCET202317 May 2023Morning ShiftMathematicsQuadratic EquationActual

If the sum of the cubes of the roots of the equation x^3-a x^2+b x-c=0 is zero, then a^3+3 c=

Options

  1. A-2 a b
  2. B2 ab
  3. C-3 a b
  4. D3 a b

Correct answer

D. 3 a b

Step-by-step solution

Given: x^3-a x^2+b x-c=0 ...(i) Let , & are the roots equation (i), we get aligned & + + =a & + + =b & =c aligned Also, given: ^3+ ^3+ ^3=0 aligned & ( + + ) ( ^2+ ^2+ ^2- - - )+3 =0 & a (( + + )^2-3( + + ) )+3 c=0 & a [a^2-3 b ]+3 c=0 & a^3-3 a b+3 c=0 a^3+3 c=3 a b aligned

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