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Chapter 4: Q. 60 (page 210)

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

f(x)=x4+1.2x3-7.46x2-4.692x+15.2881

Short Answer

Expert verified

The real zeros offafter rounding it two decimal places are-2.3and1.7.

Step by step solution

01

Step 1. Given Information

The given function isf(x)=x4+1.2x3-7.46x2-4.692x+15.2881.

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 of f is 1 witha3=1.2,a2=-7.46,a1=-4.692,anda0=15.2881.

03

Step 3. Evaluate the expressions using the formula 

So,

Max,{1,1.2+-7.46+-4.692+15.2881}=Max{1,28.6401}=28.64011+Max{1.2,-7.46,-4.692,15.2881}=1+15.2881=16.2881

The smaller of two numbers, 16.2881is the bound.

Every real zero of f liesbetween-16.2881and16.2881.

04

Step 4. Sketch the graph of the polynomial 

From the graph, we conclude that f touches the x-axis at 1.7and-2.3.

Andf(1.7)=0,f(-2.3)=0

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