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Chapter 4: Q. 42 (page 194)

In Problems 41鈥� 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros:-2,2,3;degree3

Short Answer

Expert verified

The polynomial function isfx=x3-3x2-4x+12

Step by step solution

01

Step 1. Given Information

The zeros of the polynomial-2,2,3and degree is 3

02

Step 2. Forming a Polynomial Function

If ris a real zero of a polynomial function f,then x-ris a factor of f.This means thatx--2=x+2,x-2,x-3are factor off.As a result, any polynomial function of the formfx=ax+2x-2x-3

03

Step 3. Solving polynomial function

fx=x+2x-2x-3fx=x2-4x-3fx=x3-3x2-4x+12

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Most popular questions from this chapter

Find the domain of the rational function.

Hx=3x2+xx2+4

In Problems 57鈥� 62, find the real zeros of f. If necessary, round to two decimal places.

f(x)=x3+3.2x2-16.83x-5.31

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

Solve the given inequality algebraically.

x3>1

Find the real zeros of f. Use the real zeros to factor f.

f(x)=x3+6x2+6x-4
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