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AP EAMCET20228 Jul 2022Evening ShiftMathematicsQuadratic EquationActual

aligned & x^2+1 x^4+4 = A x+B x^2-2 x+2 + C x+D x^2+2 x+2 & 3 A+2 B+3 C= aligned

Options

  1. A-D
  2. BD
  3. C2 D
  4. D-2 D

Correct answer

C. 2 D

Step-by-step solution

x^2+1 x^4+4 = A x+B x^2-2 x+2 + C x+D x^2+2 x+2 x^2+1 x^4+4 = (A x+B) (x^2+2 x+2 )+(C x+D) (x^2-2 x+2 ) (x^2+2 )^2-(2 x)^2 x^2+1=(A+C) x^3+(2 A+B-2 C+D) x^2+(2 A+2 B+2 C-2 D) x+(2 B+2 D) On comparing both sides, A+C=0 A=-C, 2 B+2 D=1 and 2 A+B-2 C+D=1 aligned & 2(A-C)+B+D=1 & 4 A+ ( 1 2 )=1 & 4 A=1- 1 2 = 1 2 & A= 1 8 and C=- 1 8 aligned Now, 2 A+2 B+2 C-2 D=0 aligned & 2(A+C)+2(B-D)=0 & B=D & and 2 B+2 D=1 aligned 4 B=1 B=D= 1 4 Now, 3 A+2 B+3 C=2 B [ 3 A+3 C=0]=2 D

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