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AP EAMCET202124 Aug 2021Morning ShiftMathematicsDifferential EquationsActual

Which of the following is an improper rational fraction?

Options

  1. Ax^2+1 (x^2+2 ) (x^2+x+1 )
  2. Bx^2+1 (x+3) (x^2-x+1 )
  3. Cx (x^2+3 x+1 )
  4. Dx^2+1 x^2-1

Correct answer

D. x^2+1 x^2-1

Step-by-step solution

For improper fraction [ p(x) q(x) ] (i) P(x) and q(x) both are polynomial. (ii) Degree of p(x) degree of q(x) . Option (a) x^2+1 (x^2+1 ) (x^2+x+1 ) = p(x) q(x) Degree of p(x)=2 Degree of q(x)=4 It is not improper fraction. Option (b) x^2+1 (x+3) (x^2-x+1 ) = p(x) q(x) Degree of p(x)= 2 Degree of q(x)=32 < 3 It is not improper fraction. Option (c) x x^2+3 x+1 = p(x) q(x) Degree of p(x)=1 Degree of q(x)=21 < 2 It is not improper fraction. Option (d) p(x) q(x) = x^2+1 x^2-1 Degree of p(x)=2= degree of q(x) It is impr

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