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Lesson: Upper and Lower Bound Tests for Polynomial Functions

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.

Worksheet • 3 Questions

Q1:

Rania is trying to find zeros in the function . She has used synthetic division to find for , , 1, and 3.

Use her results to state an interval in which all real zeros of lie.

  • A
  • B
  • C
  • D
  • E

Q2:

Using synthetic division and the upper and lower bound tests, find all real zeros of the function 𝑓 ( 𝑥 ) = 4 𝑥 + 𝑥 − 2 7 𝑥 + 1 8 𝑥 4 3 2 .

  • A − 3 , 0 , 3 4 , 2
  • B − 3 , 0 , − 4 3 , − 2
  • C 3 , 3 4 , 2
  • D − 3 , 0 , 4 3 , 2
  • E 3 , 0 , − 3 4 , − 2

Q3:

Consider the function .

Nabil is using synthetic division to help him find real zeros of .

What can he conclude about −5?

  • AThat it is a lower bound on the interval in which all real zeros lie
  • BThat it is an upper bound on the interval in which all real zeros lie
  • CThat it is neither upper bound nor lower bound on the interval in which all real zeros lie
  • DThat it is a real zero of

What can he conclude about 2?

  • AThat it is a lower bound on the interval in which all real zeros lie
  • BThat it is a real zero of
  • CThat it is the only real zero of

Find all the real zeros of .

  • A−4, 2
  • B−2, 2
  • C1, 4
  • D−13, 1
  • E2, 13
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