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Mathematics
Problem
The condition that the root of
x
3
+
3
p
x
2
+
3
q
x
+
r
=
0
x^3 + 3px^2 + 3qx + r = 0
x
3
+
3
p
x
2
+
3
q
x
+
r
=
0
are in H.P. is: (a)
2
p
3
−
3
p
q
r
+
r
2
=
0
2p^3 - 3pqr + r^2 = 0
2
p
3
−
3
pq
r
+
r
2
=
0
(b)
3
p
3
−
2
p
q
r
+
p
2
=
0
3p^3 - 2pqr + p^2 = 0
3
p
3
−
2
pq
r
+
p
2
=
0
(c)
2
q
3
−
3
p
q
r
+
r
2
=
0
2q^3 - 3pqr + r^2 = 0
2
q
3
−
3
pq
r
+
r
2
=
0
(d)
r
3
−
3
p
q
r
+
2
q
3
=
0
r^3 - 3pqr + 2q^3 = 0
r
3
−
3
pq
r
+
2
q
3
=
0
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