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AP EAMCET202120 Aug 2021Evening ShiftMathematicsQuadratic EquationActual

If 2 x 4 - x 3 + 3 x 2 - x + 4 x 2 - 3 x + 2 = f ( x ) + A x - 1 + B x - 2 then

Options

  1. Af ( x ) = 2 x 2 + 5 x + 14 , A + B = 39
  2. Bf ( x ) = 2 x 2 - 5 x + 14 , A + B = 31
  3. Cf ( x ) = 2 x 2 + 5 x + 14 , A + B = 31
  4. Df ( x ) = 2 x 2 + 5 x + 14 , A = 4 , B = 35

Correct answer

C. f ( x ) = 2 x 2 + 5 x + 14 , A + B = 31

Step-by-step solution

2 x 4 - x 3 + 3 x 2 - x + 4 x 2 - 3 x + 2 ⇒ q u o t i e n t = 2 x 2 + 5 x + 14 ⇒ r e m a i n d e r = 31 x - 28 ∴ f x = 2 x 2 + 5 x + 14         r e m a i n d e r = 31 x - 28           A + B = 31 ..

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