If an integer n, greater

Question

If an integer $n$, greater than $8$, is a solution of the equation $x^2 -ax + b=0$ and the representation of a in base n is $18$, then what is the base $n$ representation of $b$?

I honestly am so lost I have no clue how to do this.

Answer 1

We are told that $a=18_n=n+8$, and that

$$0=n^2-an+b=n^2-(n+8)n+b.$$

Hence

$$b=8n=80_n.$$