Suppose the quadratic x^2 + bx + c equals 0 when x = r or x = s. If \(r^2s+s^2r=10 \), and b and c are integers, find all possible ordered pairs (b,c).
Sum of the roots = -b
Product of the roots = c
So
r^2s + s^2 r = 10
rs ( r + s) = 10
rs r + s b c
-10 -1 1 -10
-5 - 2 2 - 5
-2 - 5 5 - 2
-1 -10 10 - 1
1 10 -10 1
2 5 - 5 2
5 2 - 2 5
10 1 - 1 10
