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Find the range of value of \(\lambda\) for which the expression \(\dfrac{2x^2-5x+3}{4x-\lambda}\) can take all real values for ...

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If \(\sum\limits_{k=1}^{20}\frac{k^2-\frac12}{k^4+\frac14}=\frac{A}{B}\), where \(A\) and \(B\) are relatively coprime positive integers., find \(A\)

\[\large \dfrac{x^8+6x^4+3x^3-14x+6}{x^4+3x^3-8x^2-5}\]

For how many real values of \(x\) is the above expression undefined?

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