182
L17
Rational Inequalities;
Zeros of a Polynomial Function
S
olving Rational Inequalities
1. Get all terms on the left side of the inequality with a 0
on the right side and simplify the lefthand side into a
single
fraction. Write the domain
. Reduce the fraction.
2. Find all real zeros
of the numerator and denominator
.
Determine their multiplicities.
3. Divide a real line into intervals using the zeros
found
in Step 2 and the numbers that are not in the domain
.
Label an endpoint as
•
if it is to be included in the
answer and label it as
D
if it is not.
Note:
Zeros of the denominator are never included!
Zeros of the numerator which are in the domain
are
included if and only if the inequality is non strict (
≤
,
≥
).
4.
Use the end behavior of the polynomials in the
numerator and denominator to find the sign of the
fraction on the rightmost interval (when
x
→ +∞
).
5.
Set the signs on each other interval by moving from
the right to the left and changing/not changing the
sign depending on multiplicity.
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 Summer '08
 GERMAN
 Calculus, Fundamental Theorem Of Algebra, Division, Inequalities, Complex number, Zeros Theorem

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