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AP EAMCET2015MathematicsQuadratic Equation

If a, b, c are distinct and the roots of (b-c) x^2+(c-a) x+(a-b)=0 are equal, then a, b and c are in

Options

  1. Aarithmetic progression
  2. Bgeometric progression
  3. Charmonic progression
  4. Darithmetico-geometric progression

Correct answer

A. arithmetic progression

Step-by-step solution

Given that the roots of equation (b-c) x^2+(c-a) x+(a-b)=0 are equal, so aligned & D=0 & (c-a)^2-4(a-b)(b-c)=0 & c^2+a^2-2 c a-4 a b+4 a c+4 b^2=0 & c^2+a^2+2 a c+4 b^2-4 b(c+a)=0 & (c+a)^2+(2 b)^2-2 2 b(c+a)=0 & [(c+a)-(2 b)]^2=0 & c+a-2 b=0 & 2 b=a+c aligned Hence, we can conclude that a, b and c are in AP.

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