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4 – 5: Locating Zeros of a Polynomial Function

So far, all of the methods we’ve used to find zeros/roots/solutions will only find those that are rational. This

means they must be whole numbers or fractions. But what if the roots are irrational?

For example: x =

When finding zeros by hand, we can only estimate irrational zeros by finding which numbers they fall between.

1. Determine between which consecutive integers the real zeros of the function

f(x) = x3 – 4x2 – 2x + 8 are located.

By Hand: By Calculator:

x 1 -4 -2 8

-3

-2

-1

0

1

2

3

4

5

CALULATOR TIP: To get a more accurate answer, you can change the interval on the table on your

calculator or use the CALC feature 2:Zero.

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2. Approximate the real zeros of f(x) = 12x3 – 19x2 – x + 6 to the nearest tenth.

3. The function models the

unemployment rate where x represents the number of months since October 2015. Use the

model to determine when the unemployment rate will be 2.5%.

When using synthetic division, you must pick your own x-values to test. It can be tricky to know where to start

and where to end.

The _____________________________________________________________can help you with this issue.

4. Use the Upper Bound and Lower Bound Theorems to find an upper and lower bound of the

zeros of f(x) = x3 + 3x2 – 5x – 10.