If the function f given by f(x)=x^3-3(a-2) x^2+3 a x+7, for some a ∈ R is increasing in (0, 1] and decreasing in [1,5), then a root of the equation,…

If the function $\displaystyle f$ given by $\displaystyle f(x)=x^3-3(a-2) x^2+3 a x+7$, for some $\displaystyle a \in \mathbf{R}$ is increasing in ($\displaystyle 0$, $\displaystyle 1$] and decreasing in $\displaystyle [1,5)$, then a root of the equation, $\displaystyle \frac{f(x)-14}{(x-1)^2}=0(x \neq 1)$ is :