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Chapter 4: Q. 21 (page 245)

Find bounds to the real zeros of each polynomial function. Obtain a complete graph of f using a graphing utility.

f(x)=x3-x2-4x+2

Short Answer

Expert verified

Every zero of polynomial lies between -5and+5and the graph is

Step by step solution

01

Step 1. Given Information

The given polynomial isf(x)=x3-x2-4x+2

02

Step 2. Explanation

The leading coefficient of the polynomial is 1 with other coefficients as a2=-1,a1=-4,a0=2

On applyiing the Max formula, we will find the bounds of the given polynomial.

role="math" localid="1646152870016" Max1,|a0|+|a1|+....+|an-1|=Max1,|2|+|-4|+|-1|=Max{1,2+4+1}=Max{1,7}=71+Max|a0|,|a1|,....|an-1|=1+Max{|2|,|-4|,|-1|}=1+Max{2,4,1}=1+4=5

The smaller of the two numbers which means 5 is the bound of the polynomial.

So, every polynomial exist between-5and+5

03

Step 3. Graph

The graph of the given polynomial is

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