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Find the values of a for which one root ...

Find the values of `a` for which one root of equation `(a-5)x^(2)-2ax+a-4=0` is smaller than 1 and the other greater than 2.

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To solve the problem, we need to analyze the quadratic equation given by: \[ (a-5)x^2 - 2ax + (a-4) = 0 \] We want to find the values of \( a \) such that one root is less than 1 and the other root is greater than 2. ...
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