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AP EAMCET202018 Sep 2020Morning ShiftMathematicsQuadratic EquationActual

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. A(4 C )
  2. B(4 C+1 )
  3. C(3 C )
  4. D(2 C )

Correct answer

D. (2 C )

Step-by-step solution

It is given that, ( aligned & x^2+x+1 x^2+2 x+1 =A+ B x+1 + C (x+1)^2 & x^2+x+1=A (x^2+2 x+1 )+B(x+1)+C & x^2+x+1=A x^2+(2 A+B) x+(A+B+C) aligned ) On comparing the coefficient of different terms, we get (A=1,2 A+B=1 ) and (A+B+C=1 ) ( aligned & B & =-1, and C=1 & A-B & =2=2 C. aligned )

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