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Chapter 4: Q. 59 (page 210)

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

f(x)=x4-1.4x3-33.71x2+23.94x+292.41

Short Answer

Expert verified

The real zeros offafter rounding it two decimal places are-3.8and4.5.

Step by step solution

01

Step 1. Given Information 

The given function is f(x)=x4-1.4x3-33.71x2+23.94x+292.41

We have to find the real zeros and round them to two decimal places.

02

Step 2. Determine the bounds on the zeros of f  

The leading coefficient off is1witha3=-1.4,a2=-33.71,a1=23.94,a0=292.41

03

Step 3. Evaluate the expressions using the formula 

So,Max,{1,-1.4+-33.71+23.94+292.41}=Max(1,351.46}=351.461+Max{-1.4,-33.71,23.94,292.41}=1+292.41=293.41

The smaller of two numbers, 293.41is the bound.

Every real zero of flies between

04

Step 4. Sketch the graph of the polynomial 

From the graph, we conclude that f touches the x-axis at -3.8and4.5

Andf(-3.8)=0,f(4.5)=0

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