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?
Given any two polynomials in a single variable it is always
possible to eliminate the variable and obtain a formula showing the
relationship between the two polynomials. Try this one.
To find the integral of a polynomial, evaluate it at some special
points and add multiples of these values.
These are well known results found in many text books and you
will find proofs in some problems on this website. See Picture Story and Natural