# Least Negative Most Positive?

Algebra Level 5

Let $$\alpha$$, $$\beta$$ and $$\gamma$$ be the real roots of the cubic equation $$x^3-7x^2+ax+50=0$$, and their absolute values be the roots of another cubic $$x^3-bx^2+cx-d=0$$. Find the minimum integral value of $$b+d$$.

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