AP EAMCET201726 Apr 2017Morning ShiftMathematicsBasics of MathematicsActual
If 5 x^2+2 x^3+x = A₁ x + A₂ x+A₃ x^2+1 , then (A₁, A₂, A₃ )=
Options
- A(0, 2, 3)
- B(3, 0, 2)
- C(2, 3, 0)
- D(2, 0, 3)
Correct answer
C. (2, 3, 0)
Step-by-step solution
aligned & Given that, 5 x^2+2 x^3+x = A₁ x + A₂ x+A₃ x^2+1 & 5 x^2+2 x (x^2+1 ) = A₁ (x^2+1 )+ (A₂ x+A₃ ) x x (x^2+1 ) & 5 x^2+2=A₁ (x^2+1 )+A₂ x^2+A₃ x & 5 x^2+2= (A₁+A₂ ) x^2+A₃ x+A₁ aligned On comparing the coefficients of x^2, x and constant term, we get A₁=2 ; A₂=3 and A₃=0 aligned & Given that, 5 x^2+2 x^3+x = A₁ x + A₂ x+A₃ x^2+1 & 5 x^2+2 x (x^2+1 ) = A₁ (x^2+1 )+ (A₂ x+A₃ ) x x (x^2+1 ) & 5 x^2+2=A₁ (x^2+1 )+A₂ x^2+A₃ x & 5 x^2+2= (A₁+A₂ ) x^2+A₃ x+A₁ aligned On comparing the coefficients of x^2, x and con