Zeros of polynomial functions

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Presentation transcript:

Zeros of polynomial functions

Real Zeros Recall that a polynomial function of degree n can have at most n real zeros. These real zeros can be rational or irrational. The Rational Zero Theorem describes how the leading coefficient and constant term of a polynomial function with integer coefficients can be used to determine a list of all possible zeros.

Rational Zero Theorem

Leading coefficient equal to 1

Leading coefficient not 1

Upper and lower bound tests

Upper and lower bound tests

To make use of the upper and lower bound tests, use these steps: Graph the function to determine an interval in which the zeros lie. Using synthetic substitution, confirm that the upper and lower bounds of your interval are in fact upper and lower bouns of the function by applying the upper and lower bound tests. Use the Rational Zero Theorem to help find all the real zeros.

Use the upper and lower bound tests