AP EAMCET · Maths · Quadratic Equation
If \(\frac{x^3+x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}=\frac{A x+B}{x^2+2}+\frac{C x+D}{x^2+3}\), then \(\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}=\)
- A 1
- B 4
- C 3
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
\(x^3+x^2+1 = (Ax+B)(x^2+3) + (Cx+D)(x^2+2)\) \(x^3+x^2+1 = (A+C)x^3 + (B+D)x^2 + (3A+2C)x + (3B+2D)\) \(A+C=1\) \(B+D=1\) \(3A+2C=0\) \(3B+2D=1\) \(A=-2, C=3\) \(B=-1, D=2\) \(A+B+C+D = -2+(-1)+3+2 = 2\)
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