x
=
±
2
,
±
1
EXPLANATION
Let
y
=
x
2
.
y
2
−
5
y
+
4
=
0
This is a nice and simple trinomial to factor.
(
y
−
4
)
(
y
−
1
)
=
0
y
=
4
or
y
=
1
We now reverse our substitution.
x
2
=
4
or
x
2
=
1
x
=
±
2
or
±
1
The graph of the function
f
(
x
)
=
x
4
−
5
x
2
+
4
confirms that there are zeroes at
x
=
±
2
and
±
1
.
graph{x^4 - 5x^2 + 4 [-10, 10, -5, 5]}
