5.6A Rational Zeros Theorem. Number System REALIMAGINARY RATIONAL IRRATIONAL i end ordon’t enda+bi Repeatdon’t repeat Integerssquare roots Fractionsπ.

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Presentation transcript:

5.6A Rational Zeros Theorem

Number System REALIMAGINARY RATIONAL IRRATIONAL i end ordon’t enda+bi Repeatdon’t repeat Integerssquare roots Fractionsπ or e

Rational Zeros Test

Examples: List the POSSIBLE Rational Zeros

Examples: List POSSIBLE Rational Zeros

Finding ALL REAL Solutions: A graph can shorten your list. Focus on #’s in list that appear to be where the graph touches x-axis (x-intercepts) Synthetically divide by a GOOD zero from graph. Remainder = ZERO if it is a solution – If new quotient is degree of 2: factor & solve or quadratic formula to solve – If new quotient is degree of 3 or more, synthetically divide NEW quotient by another GOOD zero from graph, & solve. – IF no graph given: choose #’s from list & synthetically divide until Remainder = zero, then synthetically divide NEW quotient by more #’s from your list until you can factor & solve to find ALL solutions (or quadratic formula)

Examples: Shorten list & find ALL real zeros

Example: Shorten list and find ALL Real Zeros