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Chapter 4: Q. 7 (page 209)

If a function f, whose domain is all real numbers, is even and if 4is a zero of f, then is also a zero.

Short Answer

Expert verified

If a function fwhose domain is all real numbers, is even and if 4is a zero of f, then -4is also a zero.

Step by step solution

01

Step 1. Given information.

The given statement is

If a function f, whose domain is all real numbers, is even and if 4is a zero of f, then is also a zero.

02

Step 2. Solving.

Here it is given that the function is even then,

f(x)=f(-x)

Since f(4)=0is the zero of the function then,

f(-4)=0

Therefore the other root is-4.

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Most popular questions from this chapter

Make up a polynomial function that has the following characteristics: crosses the x-axis at -1and 4, touches the x-axis at 0and 2, and is above the x-axis between 0and2. Give your polynomial function to a fellow classmate and ask for a written critique

In Problems 21鈥�32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=-4x3-x2+x+2

In Problems 21鈥�32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=2x5-x4-x2+1

Analyze each polynomial function using Steps 1through 8:

f(x)=x4+x3-3x2-x+2.

In Problems 63鈥�72, find the real solutions of each equation.

x4-x3+2x2-4x-8=0
See all solutions

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