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AP EAMCET201923 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

Let (a, b, c, d R ). If the equations (2 b x^2+3 c x-d=0 ) and (2 a x^2+3 b x+4 c=0 ) have a common root and ( 4 b c+a d k (b^2-a c ) = b d+4 c^2 4 b c+a d^ ), then (k= )

Options

  1. A( 9 2 )
  2. B( 2 9 )
  3. C( 1 9 )
  4. D( 1 3 )

Correct answer

A. ( 9 2 )

Step-by-step solution

It is given that the given quadratic equations (2 b x^2+3 c x-d=0 and ) (2 a x^2+3 b x+4 c=0 ) have a common root, ( (6 b^2-6 a c ) (12 c^2+3 b d )=(8 b c+2 a d)^2 ) Then, (6 (b^2-a c ) 3 (4 c^2+b d )=4(4 b c+a d)^2 ) ( ) ( 4 b c+a d 9 2 (b^2-a c ) = b d+4 c^2 4 b c+a d ) On comparing, we get (k= 9 2 ) Hence, option (a) is correct.

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