The best way is to recognise that, if
x
=
5
is a root, then
x
−
5
=
0
, and ditto for the other two roots. So we have
x
−
5
,
x
−
i
,
x
+
i
all equalling zero. To find our polynomial, we just multiply the three terms together:
(
x
−
5
)
(
x
−
i
)
(
x
+
i
)
=
(
x
2
−
i
x
−
5
x
+
5
i
)
(
x
+
i
)
=
x
3
+
i
x
2
−
i
x
2
−
(
i
2
)
x
−
5
x
2
−
5
i
x
+
5
i
x
+
5
i
2
which simplifies to
x
3
−
5
x
2
+
x
−
5
.
[2.01] a = a is an example of which algebraic property?
Reflexive Property
2. [2.01] 3(a + b) = 3a + 3b is an example of which algebraic property?
Distributive Property
3. [2.01] Solve: x − 2 = −6
−4
4. [2.01] Solve: = 10
lacking information
5. [2.02] Solve: + 5 = 12
Lacking info
6. [2.02] Solve: −2(x − 8) = −10
13
7. [2.02] Solve: 8x − 10 + 18 = 24
2
Answer:
C, (–7.5, –5)
Step-by-step explanation:
