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AP EAMCET2015MathematicsQuadratic Equation

If the roots of x^3-k x^2+14 x-8=0 are in geometric progression, then k is equal to

Options

  1. A-3
  2. B7
  3. C4
  4. D0

Correct answer

B. 7

Step-by-step solution

Given equation, x^3-k x^2+14 x-8=0 Roots of the above equation is in G.P. So let a r , a and a r are the roots of equation. Then, product of roots aligned & a r a a r= D A a r a a r=8 a^3=8 & a=2 aligned Therefore, at a=2 is the root of equation. aligned & x^3-k x^2+14 x-8=0 & (2)^3-k(2)^2+14(2)-8=0 & 8-4 k+28-8=0 k=7 aligned

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