Question

Question #44ed3

Answer 1

The zeros occur at `x = -4` and `x = -7`. Please observe that we have discarded `x = -3` because it is one of the values that are not allowed.

Explanation:

Given:

`f(x) = (x^3+14x^2+61x+84)/(x^3+4x^2−69x−216) = 0`

Factor the denominator so that we may restrict the domain to prevent division by 0:

`f(x) = (x^3+14x^2+61x+84)/((x-8)(x+3)(x+9)) = 0`

This means that x must not equal `8,-3 or -9`

`f(x) = (x^3+14x^2+61x+84)/((x-8)(x+3)(x+9)) = 0;x !=8,-3,-9`

Factor the numerator:

`f(x) = ((x+3)(x+4)(x+7))/((x-8)(x+3)(x+9)) = 0;x !=8,-3,-9`

The zeros occur at `x = -4` and `x = -7`. Please observe that we have discarded `x = -3` because it is one of the values that are not allowed.