Question 3

a, b, c, d, e, f are real numbers such that the polynomial $$P(x) = x^8 - 4x^7 + 7x^6 + ax^5 + bx^4 + cx^3 + dx^2 + ex + f$$ factorises into eight linear factors $$(x-x_i)$$ with $$x_i>0$$ for $$i=1,2,3,\ldots,8$$. Find the possible values of the constant f.


Correct Answer: 0.00390625

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