Locating Real Zeros of Polynomials

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Presentation transcript:

Locating Real Zeros of Polynomials MAT 102 ~ College Algebra ~ Lesson 5.3

Rational Root Theorem If f(x) is a polynomial of integer coefficients, then any rational root zero of f must be in the form of p/q, where p is a factor of a0 (last number) and q is a factor of the leading coefficient an

Use the rational root theorem to list all possible rational zeros, then locate actual zeros

Intermediate Value Theorem If f(x) is a polynomial, and a and b are real numbers with a < b . If f(a) and f(b) differ in signs, then there is at least one point c, such that a < c < b and f(c) = 0. That is, at least one zero of f lies between a and b.

Show that f(x) has a zero between the given values and approximate that zero to the nearest tenth

Solve

Recommended Practice: Pg Recommended Practice: Pg. 401 – 404 # 1 – 24, 57 – 62, 64 – 83 Required Certification 5.3 Due: ______________ Test # 4: Wed. 12/9/09 4.4, 4.5, 4.6, 5.1, 5.2, 5.3