Problem: If an integer nnn greater than 8 is a solution of the equation x2+ax+b=0x^{2} + a x+b=0x2+ax+b=0 and the representation of aaa in the base nnn numeration system is 18, then the base nnn representation of bbb is
Answer Choices:
A. 181818
B. 282828
C. 808080
D. 818181
E. 280280280 Solution:
b=an−n2=(18)nn−n2=(n+8)n−n2=(80)nb=a n-n^{2}=(18)_{n} n-n^{2}=(n+8) n-n^{2}=(80)_{n}b=an−n2=(18)nn−n2=(n+8)n−n2=(80)n.