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Dahlia Martin
Mathematics
5 January, 12:22
Graph
A third degree polynomial with 2 zeros
+1
Answers (
1
)
Karlee Cooley
5 January, 12:31
0
For a third degree polynomial, we need 3 linear factors.
Since
5
and
2
i
are roots (zeros), we know that
x
-
5
and
x
-
2
i
are factors.
If we want a polynomial with real coeficients, then the complex conjugate of
2
i
(which is
-
2
i
) must also be a root and
x
+
2
i
must be a factor.
One polynomial with real coefficients that meets the requirements is
(
x
-
5
)
(
x
-
2
i
)
(
x
+
2
i
)
=
(
x
-
5
)
(
x
2
+
4
)
=
x
3
-
5
x
2
+
4
x
-
20
Any constant multiple of this also meets the requirements.
For example
7
(
x
3
-
5
x
2
+
4
x
-
20
)
=
7
x
3
-
35
x
2
+
28
x
-
140
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