In this lesson, we will learn how to use upper and lower bound tests to verify if the given interval is the interval that contains all real zeros.
Q1:
Using synthetic division and the upper and lower bound tests, find all real zeros of the function 𝑓(𝑥)=4𝑥+𝑥−27𝑥+18𝑥.
Q2:
Hannah is trying to find zeros in the function 𝑓(𝑥)=6𝑥+19𝑥−37𝑥−62𝑥+24. She has used synthetic division to find 𝑓(𝑎) for 𝑎=−5, −2, 1, and 3.
Use her results to state an interval in which all real zeros of 𝑓 lie.
Q3:
Consider the function 𝑓(𝑥)=𝑥−4𝑥−7𝑥+74𝑥−104.
James is using synthetic division to help him find real zeros of 𝑓.
What can he conclude about −5?
What can he conclude about 2?
Find all the real zeros of 𝑓.
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