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Chapter 4: Q. 104 (page 195)

Construct a polynomial function f with the given characteristics:

Zeros: -4, -1, 2; degree: 3; y-intercept: 16.

Short Answer

Expert verified

The required polynomial is fx=-2x+4x+1x-2

Step by step solution

01

Step 1. Given information.

The following information related to the polynomial is given:

Zeros: -4, -1, 2; degree: 3; y-intercept: 16.

02

Step 2. Constructing the polynomial. 

Since all the zeros of the polynomial have a multiplicity of 1, the general 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.

Substituting the value of the zeros, we get the following:

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

The y-intercept of the polynomial can be obtained at x=0.

At x=0, we have the following:

f0=16=a0+4x+10-216=-8aa=-168a=-2

So, the expression of the polynomial will be

fx=-2x+4x+1x-2

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