Find all the value of x for which x^3(x-1)/(x-2)>0
Answers
Answer:
HEY MATE
Step-by-step explanation:
Find all the values where the expression switches from negative to positive by setting each factor equal to
0
and solving.
x
−
3
=
0
x
−
1
=
0
x
+
2
=
0
Add
3
to both sides of the equation.
x
=
3
Add
1
to both sides of the equation.
x
=
1
Subtract
2
from both sides of the equation.
x
=
−
2
Solve for each factor to find the values where the absolute value expression goes from negative to positive.
x
=
3
x
=
1
x
=
−
2
Consolidate the solutions.
x
=
3
,
1
,
−
2
Find the domain of
x
−
3
(
x
−
1
)
(
x
+
2
)
.
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(
−
∞
,
−
2
)
∪
(
−
2
,
1
)
∪
(
1
,
∞
)
Use each root to create test intervals.
x
<
−
2
−
2
<
x
<
1
1
<
x
<
3
x
>
3
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
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x
<
−
2
True
−
2
<
x
<
1
False
1
<
x
<
3
True
x
>
3
False
The solution consists of all of the true intervals.
x
<
−
2
or
1
<
x
<
3
The result can be shown in multiple forms.
Inequality Form:
x
<
−
2
or
1
<
x
<
3
Interval Notation:
(
−
∞
,
−
2
)
∪
(
1
,
3
)
image of graph