Question 9A quadratic polynomial $P(x)=ax^2+bx+c$, where $a\ne0$, has the following properties: $$P(n)=\frac1{n^2}\quad\text{for all }n=-1,2,3.$$ Determine the smallest positive value of $k$, where $k\ne2,3$, such that $P(k)=\frac1{k^2}$.