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Problem
Problem
Let
α
,
β
\alpha, \beta
α
,
β
be the roots of the equation
x
2
−
p
x
+
r
=
0
x^2 - px + r = 0
x
2
−
p
x
+
r
=
0
and
α
2
,
2
β
\frac{\alpha}{2}, 2\beta
2
α
,
2
β
be the roots of the equation
x
2
−
q
x
+
r
=
0
x^2 - qx + r = 0
x
2
−
q
x
+
r
=
0
. The value of
r
r
r
is a.
2
9
(
p
−
q
)
(
2
q
−
p
)
\frac{2}{9}(p-q)(2q-p)
9
2
(
p
−
q
)
(
2
q
−
p
)
b.
2
9
(
q
−
p
)
(
2
p
−
q
)
\frac{2}{9}(q-p)(2p-q)
9
2
(
q
−
p
)
(
2
p
−
q
)
c.
2
9
(
q
−
2
p
)
(
2
q
−
p
)
\frac{2}{9}(q-2p)(2q-p)
9
2
(
q
−
2
p
)
(
2
q
−
p
)
d.
2
9
(
2
p
−
q
)
(
2
q
−
p
)
\frac{2}{9}(2p-q)(2q-p)
9
2
(
2
p
−
q
)
(
2
q
−
p
)
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