4.5 Locating Zeros of a Polynomial Function

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Presentation transcript:

4.5 Locating Zeros of a Polynomial Function Objective: Approximate the real zeros of a polynomial function.

The Location Principle: Suppose y=f(x) represents a polynomial function with real coefficients. If a and b are two numbers with f(a) negative and f(b) positive, the function has at least one real zero between a and b. See page 237 Ex.1) Determine between which consecutive integers the real zeros of f(x)= 12x³ - 20x² - x + 6 are located.

Ex.2) Approximate the real zeros of f(x)= -3x^4 + 16x³ - 18x² + 5 to the nearest tenth. Upper Bound: An integer greater than or equal to the greatest real zero. Lower Bound: An integer less than or equal to the least real zero. Ex.3) Find the upper and lower bound of the zeros of f(x) = 6x³ - 7x² - 14x + 15