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Algebra Level 5

Let \(a, b,c\) be three real numbers such that \(a+b+c = 6\) and \( ab + bc + ca = 9.\)

If exactly one root of the equation \(x^{2} - (m+2)x+5m = 0\) lies between minimum and maximum value of \(c\), find the number of integral values of \(m\).

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