AP EAMCET202420 May 2024Evening ShiftMathematicsBasics of MathematicsActual
If x^2+3 x^4+2 x^2+9 = A x+B x^2+a x+b + C x+D x^2+c x+b then a A+b B+c C+D=
Options
- A1
- B0
- C-1
- D2
Correct answer
D. 2
Step-by-step solution
x^4+2 x^2+9 aligned & =x^4+9+6 x^2-6 x^2+2 x^2 & = (x^2+3 )^2-4 x^2= (x^2-2 x+3 ) (x^2+2 x+3 ) & x^2+3 x^4+2 x^2+9 = 1 2 ( 1 x^2-2 x+3 + 1 x^2+2 x+3 ) & x^2+3 x^4+2 x^2+9 = 1 2 x^2-2 x+3 + 1 2 x^2+2 x+3 & ~B = 1 2 , ~A =0, C =0, D = 1 2 & a=-2, b=3, c=2 & a ~A +b ~B +c C + D = 3 2 + 1 2 =2 aligned