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AP EAMCET202419 May 2024Evening ShiftMathematicsQuadratic EquationActual

If the roots of the equation x^3-13 x^2+ K x-27=0 are in geometric progression then K =

Options

  1. A-30
  2. B30
  3. C39
  4. D-39

Correct answer

C. 39

Step-by-step solution

Given the equation, x^3-13 x^2+K x-27=0 Let roots are a r , a, a r Now, a r a a r= -(-27) 1 a^3=27 a=3 and, 3 r +3+3 r= -(-13) 1 3 r +3 r=10 r=3, 1 3 Since, a r a+a a r+ a r a r=K If r=3, a=3 9 3 +27+ 27 3 =K K=39 If r= 1 3 , a =3 27+ 9 3 + 27 3 =K K=39 .

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