Find the value of the expression The expression $ax^2 + bx + 1$ takes the values $1$ and $4$ when $x$ takes the values $2$ and $3$ respectively. How can we find the value of the expression when $x$ takes the value of $4$?

Hint $\,\ f(3)=2^2,\ f(2) = 1^2,\ f(0) = (-1)^2\ $ so $\,f-(x-1)^2\!=0,\,$ having $3$ roots $\,x=3,2,0$.
