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AP EAMCET2008MathematicsQuadratic Equation

If x^2+x+1 x^2+2 x+1 =A+ B x+1 + C (x+1)^2 , then A-B is equal to

Options

  1. A4 C
  2. B4 C+1
  3. C3 C
  4. D2 C

Correct answer

D. 2 C

Step-by-step solution

x^2+x+1 x^2+2 x+1 =1- x x^2+2 x+1 Now, x x^2+2 x+1 = A (x+1) + B (x+1)^2 x=A(x+1)+B On equating the coefficient of x and constant, we get array llll & A=1 & and & A+B=0 & A=1 & and & B=-1 array From Eq. (i), aligned & x^2+x+1 x^2+2 x+1 =1- 1 (x+1) + 1 (x+1)^2 & A+ B x+1 + C (x+1)^2 & =1- 1 x+1 + 1 (x+1)^2 & A=1, B=-1 and C=1 & Now, A-B=1+1=2 & =2 C & aligned (given) Hence, option (d) is correct.

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