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Chapter 4: Q. 103 (page 195)

Construct a polynomial function f with the given characteristics:

Zeros: -3,1,4; degree: 3; y-intercept: 36.

Short Answer

Expert verified

fx=3x+3x-1x-4

Step by step solution

01

Step 1. Given information.

The following information of the polynomial is given:

Zeros: -3, 1, 4; degree: 3; y-intercept: 36

02

Step 2. Determining the form of the polynomial.

Since the multiplicity of each zero is 1 and the degree of the polynomial is 3, there are 3 different factors present in the polynomial. The factored form of the polynomial can be expressed as

fx=ax-z1x-z2x-z3--->(1)where

ais the constant of proportionality and

z1,z2,z3are the zeros of the polynomial.

By substituting the zeros in equation (1), the polynomial becomes

fx=ax--3x-1x-4fx=ax+3x-1x-4--->(2)

03

Step 3. Finding the complete form of the polynomial.

Since the y-intercept is 36, by putting x=0in equation (2), we get the following:

f0=a3-1-436=12aa=3612a=3

So, the polynomial function will be

fx=3x+3x-1x-4

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Find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f.

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