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AP EAMCET202120 Aug 2021Morning ShiftMathematicsQuadratic EquationActual

Given 3 x - 2 ( x + 1 ) 2 ( x + 3 ) = A x + 1 + B ( x + 1 ) 2 + C x + 3 , then 4 A + 2 B + 4 C

Options

  1. A5
  2. B- 5
  3. C- 3
  4. D3

Correct answer

B. - 5

Step-by-step solution

3 x - 2 ( x + 1 ) 2 ( x + 3 ) = A x + 1 + B ( x + 1 ) 2 + C x + 3 3 x - 2 ( x + 1 ) 2 ( x + 3 ) = A ( x + 1 ) ( x + 3 ) + B ( x + 3 ) + C ( x + 1 ) 2 ( x + 1 ) 2   ( x + 3 ) 3 x - 2 = A ( x 2 + 3 + 4 x ) + B ( x + 3 ) + C ( x 2 + 1 + 2 x ) Σ  of coefficients of  x 2 = 0   ⇒ A + C = 0 Σ  of coefficients of x = 3   ⇒ 4 A + B + 2 C = 3 Σ   of coefficients of constants = 0   ⇒ 3 A + 3 B + C = - 2 Equating th

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