Find all integers $ b$ and $ c$ such that the equation $ x^2 - bx + c = 0$ has two real roots $ x_1, x_2$ satisfying $ x_1^2 + x_2^2 = 5$.
Problem
Source: 2009 Puerto Rico Team Selection Test p4
Tags: algebra, trinomial, quadratic polynomial
Source: 2009 Puerto Rico Team Selection Test p4
Tags: algebra, trinomial, quadratic polynomial
Find all integers $ b$ and $ c$ such that the equation $ x^2 - bx + c = 0$ has two real roots $ x_1, x_2$ satisfying $ x_1^2 + x_2^2 = 5$.