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Mathematics
Mathematics
Problem
Given that
a
,
b
a, b
a
,
b
are integers and the two real roots
α
,
β
\alpha, \beta
α
,
β
of the equation
3
x
2
+
3
(
a
+
b
)
x
+
4
a
b
=
0
3x^2 + 3(a+b)x + 4ab = 0
3
x
2
+
3
(
a
+
b
)
x
+
4
ab
=
0
satisfy the relation
α
(
α
+
1
)
+
β
(
β
+
1
)
=
(
α
+
1
)
(
β
+
1
)
\alpha(\alpha+1) + \beta(\beta+1) = (\alpha+1)(\beta+1)
α
(
α
+
1
)
+
β
(
β
+
1
)
=
(
α
+
1
)
(
β
+
1
)
. Then, the number of ordered pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
is equal to:
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