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Chapter 4: Q. 46 (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:-3,-1,2,5;degree4

Short Answer

Expert verified

The polynomial function isfx=x4-3x3-15x2+19x+30with degree 4.

Step by step solution

01

Step 1. Given Information

The zeros of the polynomial are-3,-1,2,5and degree is 4

02

Step 2. Forming Polynomial Function

If ris a real zero of a polynomial function f,then x-ris a factor of f.This means that x--3=x+3andx+1,x-2,x-5. As a result, any polynomial function is of the formfx=x+3x+1x-2x-5

03

Step 3. Solving polynomial function

fx=x+3x+1x-2x-5fx=x2+4x+3x2-7x+10fx=x4-7x3+10x2+4x3-28x2+40x+3x2-21x+30fx=x4-3x3-15x2+19x+30

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Most popular questions from this chapter

True or False : The graph off(x)=xx-3 is above the x-axis for x<0or x>3, so the solution set of the inequality xx-3鈮�0is {x:x鈮�0orx鈮�3}..

Find the domain of the rational function.

Rx=xx3-8

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

f(x)=x3+42.2x2-664.8x+1490.4

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)=3x4-3x3+x2-x+1

For a rational functionR, if the degree of the numerator is less than the degree of the denominator, then R is ________.
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