Question 1
In this paper, let $\lfloor x\rfloor$ denote the greatest integer not exceeding $x$, and $\lceil x\rceil$ denote the smallest integer not less than $x$. For example, $\lfloor5\rfloor=5$, $\lfloor2.8\rfloor=2$, $\lfloor-2.3\rfloor=-3$; $\lceil5\rceil$, $\lceil2.8\rceil=3$, $\lceil-2.3\rceil=-2$.
On a cartesian plane, the equation $|x^2-x|=k$ has 4 distinct solutions for $a\lt k\lt b$. Find the largest possible value of $\lfloor4(b-a)\rfloor$.
On a cartesian plane, the equation $|x^2-x|=k$ has 4 distinct solutions for $a\lt k\lt b$. Find the largest possible value of $\lfloor4(b-a)\rfloor$.