Chapter 4.5, Problem 23E

To determine

To describe: and correct the error in listing the possible rational zeros of the function.

Answer to Problem 23E

The possible rational zeros of the function are $\pm 1,\pm 3,\pm 5,\pm 9,\pm 15,\pm 45$ .

Explanation of Solution

Given information:

Given function,

  $f\left(x\right)=x^3+5x^2-9x-45$

Given possible rational zeros are

  $1,3,5,9,15,45$

Calculation:

Consider the function.

  $f\left(x\right)=x^3+5x^2-9x-45$

The above function is of degree 3, so it has 3 zeros.

Here, the leading coefficient is $1$ and constant term is $-45$ .

The possible rational zeros are

  $\frac{\pm 1,\pm 3,\pm 5,\pm 9,\pm 15,\pm 45}{\pm 1}=\pm 1,\pm 3,\pm 5,\pm 9,\pm 15,\pm 45$

The correct possible rational zeros are $\pm 1,\pm 3,\pm 5,\pm 9,\pm 15,\pm 45$ .