In y = ax +b when are a, -b/a, b in arithmetic progression. The
polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2
and c be in arithmetic progression?
Find relationships between the polynomials a, b and c which are
polynomials in n giving the sums of the first n natural numbers,
squares and cubes respectively.
To find the integral of a polynomial, evaluate it at some special
points and add multiples of these values.
Good solutions to this problem were received from Tyrone of
Cyfarthfa High School in Merthyr Tydfil, and Koopa of Boston
College in the USA.
Tyrone solved the problem by relating both polynomials to