Inequalities. Interval method
Overview
Important
The interval method is a systematic way to solve inequalities involving polynomials or rational expressions. It uses the fact that the sign of a polynomial only changes at its roots (where it equals zero). By finding the roots and testing the sign in each interval between them, we can determine where the inequality holds.
Important properties
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A polynomial changes sign only at its real roots.
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The real line is divided into intervals by the roots.
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The sign of the polynomial in each interval can be determined by testing a point or by analyzing the multiplicity of roots.
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For rational expressions, include points where the denominator is zero as boundaries (excluded from the solution).