TS EAMCET · Maths · Quadratic Equation
If \(F_1\) and \(F_2\) are irreducible factors of \(x^4+x^2+1\) with real coefficients and \(\frac{x^3-2 x^2+3 x-4}{x^4+x^2+1}=\frac{A x+B}{F_1}+\frac{C x+D}{F_2}\), then \(A+B+C+D=\)
- A -2
- B 1
- C -3
- D -4
Answer & Solution
Correct Answer
(C) -3
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} x^4+x^2+1 & =x^4+x^2+x^2-x^2+1 \\ & =x^4+2 x^2+1-x^2=\left(x^2+1\right)^2-(x)^2 \\ & =\left(x^2+x+1\right)\left(x^2-x+1\right) \end{aligned} \] Now,…
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