Question 6
(a) Find the number of distinct positive real roots of $Q(x)=x^3-5x^2+4x-1$.
(b) Suppose $a,b,c,d$ are integers such that $P(x)=ax^3+bx^2+cx+d$ has three distinct positive real roots and no rational root. Find the minimum value of $S=|a|+|b|+|c|+|d|$.
(b) Suppose $a,b,c,d$ are integers such that $P(x)=ax^3+bx^2+cx+d$ has three distinct positive real roots and no rational root. Find the minimum value of $S=|a|+|b|+|c|+|d|$.