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Let $$a_i$$ for $$i = 1, 2, 3, 4, 5, 6$$ be reals. The polynomial $$f(x) = a_1 + a_2x + a_3x^2 + a_4x^3 + a_5x^4 + a_6x^5 + 7x^6 - 4x^7 + x^8$$ can be factorized into linear factors $$x - x_i$$ where $$i = 1, 2, 3, \ldots, 8$$. Find the possible values of $$a_1$$.
Correct Answer: 0.00390625
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