The functions are and
.
Given .
.
Write the inequality so that the expression is on the left side and zero is on the right side.
The function is .
Determine the real zeros ( -intercepts of the graph ) of
and the real numbers for which
is undefined.
The zeros of the function are the values of for which
.
.
Let .
Earlier we considered .
The zeros of are
and
.
Since are imiginary roots these are not to be considered.
Therefore, the zeros of the function are and
.
Use the zeros found in Step 2 to divide the real number line into intervals.
\The function intervals are and
.
Since there are real zeros, divide the
- axis into three intervals.
\
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Choose a number for in each interval and evaluate
.
Interval | \ \
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Conclusion | \
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Positive | \
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Negative \ | \
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Positive | \
(1) Draw the coordinate plane.
\(2) Graph the functions on the same graph.
Graph :
\.
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Observe the graph is below to the graph of the function
.
The inequality function interval is at
.
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The Solutions of algebraical inequality are in the interval
.
Graph :
\.