MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1
Problem
Answer the following for the quadratic polynomial x2+bx+c, where b and c are integers.
(i) State the relationship that must hold between b, c and the two integers that appear when the polynomial is written as a product of two linear factors with integer coefficients.
(ii) Explain why this relationship is necessary for the factorisation of x2+bx+c over the set of integers.