Chapter 6.3, Problem 64HP

To determine

To Find:The minimum number of the real roots and the minimum degree of the polynomial function $f\left(x\right)$ .

Answer to Problem 64HP

The function has degree of 4 and there are 4 potential zeroes.

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

$x$	-24	-18	-12	-6	0	6	12	18	24
$f\left(x\right)$	-8	-1	3	-2	4	7	-1	8	5

Calculation:

The table shows that the function has more real roots as the table shows that $f\left(x\right)$ as the potential for 5 or more zeroes and the degree is 5 or more than it. The function is 0 at five point in the table. The first is between $x=-18$ and $-12$ , $-12$ and $-6$ , $-6$ and $0$ , $6$ and 12. Thus, between $18$ and 24. Thus, the function has degree of 4 and there are 4 potential zeroes.