– 4p2 + 2xp - 1, 3x3 + 2p2 – 5xp + 3
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The roots of a quadratic
a
x
2
+
b
x
+
c
=
0
are equal when the discriminant (
b
2
−
4
a
c
) is equal to
0
In this case
a
=
1
b
=
−
2
p
c
=
(
p
+
2
)
So the discriminant is
(
−
2
p
)
2
−
4
(
1
)
(
p
+
2
)
=
4
p
2
−
4
p
−
8
which factors as
=
4
(
p
−
2
)
(
p
+
1
)
and the discriminant
=
0
if
p
=
2
or
p
=
−
1
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