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Chapter 7: Q1. (page 356)

Explain the Location Principle in your own words.

Short Answer

Expert verified

In own words: If fis continuous such that f(a)<0and f(b)>0. So f(x) is going from a negative value to positive value continuously. So, it must be zero at least somewhere in the middle.

When f(x) is zero there we get a real zero. The number of times it cuts/touches the x-axis then we get a real zero.

Step by step solution

01

Step 1. Given

Location principle.

02

Step 2. To determine

We have to explain location principle.

03

Step 3. Calculation

Location principle: Suppose y=f(x) represents a polynomial function and a and b are two numbers such that f(a)<0 and f(b)>0. Then the function has at least one real zero between a and b.

In own words: If fis continuous such that f(a)<0and f(b)>0. So f(x) is going from a negative value to positive value continuously. So, it must be zero at least somewhere in the middle.

When f(x) is zero there we get a real zero. The number of times it cuts/touches the x-axis then we get a real zero.

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Most popular questions from this chapter

OPEN ENDED Sketch the graph of an odd-degree polynomial function with a negative leading coefficient and three real roots.

Solve the equation x2+13x-3536=0 by completing the squares.

Tell whether the following statement is always, sometimes or never true. Explain. A polynomial function that has four real roots is a fourth-degree polynomial.

State the number of turning points of the graph of a fifth-degree polynomial if it has five distinct real zeroes.

For each graph,

a. Describe the end behaviour.

b. Determine whether it represents an odd-degree or an even-degree polynomial function, and

c. state the number of real zeros.
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