1. ## Cubic Functions

A cubic function f is defined for x ∈ R as f (x) = x3+ (1 - k2​)x + k, where k is a constant. Show that -k is a root of f.

How would I go about doing this? Help appreciated!

2. ## Re: Cubic Functions

Originally Posted by HelenMc9
A cubic function f is defined for x ∈ R as f (x) = x3+ (1 - k2​)x + k, where k is a constant. Show that -k is a root of f.

How would I go about doing this? Help appreciated!
What is $f(-k)=~?$

3. ## Re: Cubic Functions

Aah yes it's equal to zero because -k is a root... I know what to do now! thanks!!

4. ## Re: Cubic Functions

By the way, "root" is the wrong word here. You can find a "root" of an equation such as f(x)= 0, or a "zero" of a function, that being, of course, the root of the equation f(x)= 0.

5. ## Re: Cubic Functions

Originally Posted by HallsofIvy
By the way, "root" is the wrong word here. .
There does seem to be general agreement on that.
See zero here and root there.