Ron's Roots

Algebra Level 3

Let α\alpha and β\beta be the roots of 3x2+4x+9=0 3 x^{2} + 4x + 9 = 0. Then (1+α)(1+β) (1+ \alpha)(1 + \beta) can be expressed in the form ab\frac{a}{b}, where aa and bb are coprime positive integers. Find a+ba+b.

This problem is posed by Ron G.

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