Least Negative Most Positive?

Algebra Level 5

Let α\alpha, β\beta and γ\gamma be the real roots of the cubic equation x37x2+ax+50=0x^3-7x^2+ax+50=0, and their absolute values be the roots of another cubic x3bx2+cxd=0x^3-bx^2+cx-d=0. Find the minimum integral value of b+db+d.

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