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Mathematics
Mathematics
Problem
a
+
b
a + b
a
+
b
If
α
\alpha
α
,
β
\beta
β
are roots of the equation
2
x
2
+
6
x
+
b
=
0
2x^2 + 6x + b = 0
2
x
2
+
6
x
+
b
=
0
where
b
<
0
b < 0
b
<
0
, then find the least integral value of
(
α
2
β
+
β
2
α
)
\left(\frac{\alpha^2}{\beta} + \frac{\beta^2}{\alpha}\right)
(
β
α
2
+
α
β
2
)
.
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