Question 1
Let $a,b,c,d,e,f$ be 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 $x_i\gt 0$ for $i=1,2,\ldots,8$. Determine all possible values of $f$.
$$p(x)=x^8-4x^7+7x^6+ax^5+bx^4+cx^3+dx^2+ex+f$$
factorises into eight linear factors $x-x_i$, with $x_i\gt 0$ for $i=1,2,\ldots,8$. Determine all possible values of $f$.