# Another cubic, with interesting roots

Algebra Level 4

Let $$f(x) = x^3 + ax^2 + bx + a,$$ for some nonzero integers $$a$$ and $$b$$. Let $$r_1, r_2,$$ and $$r_3$$ be the roots of $$f(x)$$. It is given that

$(r_1 + r_2)(r_2 + r_3)(r_3 + r_1) = -1.$

Find the value of $$b$$.

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