Chapter 9.2, Problem 43E

To determine

To approximate the zeroes of f to the nearest tenth.

Answer to Problem 43E

The closest value is -0.7 and 4.3.

Explanation of Solution

Given information:

  $f(x)=x^2-5x+3$

Calculation:

The given equation is $f(x)=x^2-5x+3$

There are two intercepts: the one between 0 and 1, the 2^nd between 4 and 5.

Make a table between x - values between 0 and 1, 4 and 5. Use an increment of 0.1. Look for change of sign of the function values.

The table is

$x$	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
$f(x)$	2.51	2.04	1.59	1.16	0.75	0.36	-0.01	-0.36	-0.69

The change in sign is from 0.7.

$x$	4.1	4.2	4.3	4.4	4.5	4.6	4.7	4.8	4.9
$f(x)$	-0.69	-0.36	-0.01	0.36	0.75	1.16	1.59	2.04	2.51

The change in sign is from 4.3

The function value that are closest to 0 correspond to x -values that best approximate the zeros of the function.

The closest value is -0.7 and 4.3.