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AP EAMCET202315 May 2023Evening ShiftMathematicsQuadratic EquationActual

If x+2 x^2-3 is one of the partial fractions of 3 x^3-x^2-2 x+17 x^4+x^2-12 , then the other partial fraction of it is

Options

  1. A2 x+3 x^2-4
  2. B3 x+2 x^2+4
  3. C2 x-3 x^2+4
  4. D3 x-2 x^2-4

Correct answer

C. 2 x-3 x^2+4

Step-by-step solution

aligned & Since 3 x^3-x^2-2 x+17 x^4+x^2-12 & = 3 x^3-x^2-2 x+17 (x^2-3 ) (x^2+4 ) = x+2 x^2-3 + A x+B x^2+4 & A x+B x^2+4 = 3 x^3-x^2-2 x+17- (x^2+4 )(x+2) (x^2-3 ) (x^2+4 ) & A x+B x^2+4 = 3 x^3-x^2-2 x+17-x^3-2 x^2-4 x-8 (x^2-3 ) (x^2+4 ) & A x+B= 2 x^3-3 x^2-6 x+9 (x^2-3 ) = x^2(2 x-3)-3(2 x-3) (x^2-3 ) & A x+B=2 x-3 aligned So other partial fraction = 2 x-3 x^2+4

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