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Chapter 7: Q4. (page 350)

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.

Short Answer

Expert verified

The given statement is sometimes true.

Step by step solution

01

Step 1. Given

Given statement is: A polynomial function that has four real roots is a fourth-degree polynomial.

02

Step 2. To determine

We have to tell and explain whether the following statement is always, sometimes or never true.

03

Step 3. Calculation

We can draw an even polynomial with four real roots. For example:

This graph is of a 4th degree polynomial. And it has 4 real roots -2,-1,1,2.

We can also draw an odd polynomial with four real roots. For example:

This graph is of a 5th degree polynomial. And it has 4 real roots -2,-1,1,2.

So, the given statement is sometimes true.

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Most popular questions from this chapter

Find p4andp-2 for the function px=x5-x2.

BUSINESS

Becca is writing a computer program to find the salaries of her

employees after their annual raise. The percent of increase is represented by p.

Marty’s salary is $23,450now. Write a polynomial to represent Marty’s salary

after one year and another to represent Marty’s salary after three years. Assume

that the rate of increase will be the same for each of the three years.

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.

Graph the function y=x2+4 by making table of values.

State the degree and leading coefficient of polynomial c2+c-1c in one variable. If it is not a polynomial in one variable, explain why.
See all solutions

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