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Problem
Problem
If
a
+
b
+
c
=
0
a+b+c=0
a
+
b
+
c
=
0
and
a
,
b
,
c
a, b, c
a
,
b
,
c
are rational. Prove that the roots of the equation
(
b
+
c
−
a
)
x
2
+
(
c
+
a
−
b
)
x
+
(
a
+
b
−
c
)
=
0
(b+c-a)x^2 + (c+a-b)x + (a+b-c) = 0
(
b
+
c
−
a
)
x
2
+
(
c
+
a
−
b
)
x
+
(
a
+
b
−
c
)
=
0
are rational.
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