Find the zeros: Includes a cube

[Bo_]

Homework Statement

Find the zeros of the function algebraically.

Homework Equations

f(x) = 4x^3 - 24x^2 - x + 6

The Attempt at a Solution

If all quantities had an x in them, I'd just factor out and x, and treat it as a quadratic. But that freaking 6 is ruining my plan and I'm stuck.

 

[Dick]

You'll have to try and factor it. Look for a rational root.

 

[Bo_]

k, so I factored it to (1 - 4x^2)(-x - 6)

...what are the zeros? 6? Someone help me interpret that...pleeease.

 

[Dick]

How did you get the (-x-6) factor? I get just (x-6). Or did you mean to write (-x+6)? Then to find the roots, just set each factor equal to zero, right? The product of things can only be zero if one of the things is zero.

 

[Bo_]

Damnit, yeah I meant to have (x - 6).

 

[Bo_]

Okay so they're 6, +1/2, -1/2. Correct if I'm wrong. If not, thanks.

 

[Dick]

They are correct. Didn't want to just leave you hanging. You can also check for yourself, just put those values into the polynomial and see if you get zero.