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Mathematics
Problem
Suppose the quadratic
x
2
+
b
x
+
c
x^2 + bx + c
x
2
+
b
x
+
c
equals 0 when
x
=
r
x = r
x
=
r
or
x
=
s
x = s
x
=
s
. If
r
2
s
+
s
2
r
=
10
r^2s + s^2r = 10
r
2
s
+
s
2
r
=
10
, and
b
b
b
and
c
c
c
are integers, find all possible ordered pairs
(
b
,
c
)
(b, c)
(
b
,
c
)
.
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