Consider a polynomial function of degree 4, given by:
P
(
x
)
=
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
P(x)=ax
4
+bx
3
+cx
2
+dx+e
Suppose the graph of the polynomial passes through the points
(
−
1
,
5
)
,
(
1
,
11
)
,
(−1,5),(1,11), and
(
2
,
8
)
(2,8).
Which of the following options represents the complete solution to the given data?
[
a
b
c
d
e
]
=
[
0
0
−
2
3
10
]
u
+
[
0
1
−
2
−
1
2
]
v
+
[
−
1
0
−
5
0
4
]
,
u
,
v
∈
R
a
b
c
d
e
=
0
0
−2
3
10
u+
0
1
−2
−1
2
v+
−1
0
−5
0
4
,u,v∈R
[
a
b
c
d
e
]
=
[
1
0
5
0
4
]
u
+
[
0
1
2
−
1
2
]
v
+
[
0
0
2
3
10
]
,
u
,
v
∈
R
a
b
c
d
e
=
1
0
5
0
4
u+
0
1
2
−1
2
v+
0
0
2
3
10
,u,v∈R
[
a
b
c
d
e
]
=
[
1
0
−
5
0
4
]
u
+
[
0
1
−
2
−
1
2
]
v
+
[
0
0
−
2
3
10
]
,
u
,
v
∈
R
a
b
c
d
e
=
1
0
−5
0
4
u+
0
1
−2
−1
2
v+
0
0
−2
3
10
,u,v∈R
[
a
b
c
d
e
]
=
[
1
0
−
5
3
4
]
u
+
[
0
1
−
2
−
1
2
]
v
+
[
0
0
−
2
0
10
]
,
u
,
v
∈
R
a
b
c
d
e
=
1
0
−5
3
4
u+
0
1
−2
−1
2
v+
0
0
−2
0
10
,u,v∈R
Mathbot Says...
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