If one of the roots of the equation \(6x^3 - 25x^2 + 2x + 8 = 0\) is an integer and \(\alpha>0\), \(\beta<0\) are the other two roots, then \( \frac{4}{\alpha} + \frac{1}{\beta} = \)
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When dealing with cubic polynomials where one root is known, use Vieta's formulas to find the sum and product of the other two roots. This avoids polynomial long division and quickly sets up a quadratic equation for the remaining roots.