SOLUTION: Please help me solve this equation by finding all zeros: f(x)= x^3-6x^2+4x-24

Question 196678: Please help me solve this equation by finding all zeros: f(x)= x^3-6x^2+4x-24
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please help me solve this equation by finding all zeros: f(x)= x^3-6x^2+4x-24
---------
I graphed it and found x=6 is a zero:
Using synthetic division I get:
6)....1....-6....4....-24
.......1.....0.....4...|..0
Quotient: x^2+4
---------------
Other Zeros:
x^2+4 = 0
(x+2i)(x-2i) = 0
x = 2i or x = -2i
======================
Final Answer:
x = 6 or x = 2i or x = -2i
================================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Recall that the zeros are the values of "x" that make

Start with the given function

Plug in

Rearrange the equation

Group the terms into pairs

Factor the GCF from the first group

Factor the GCF from the second group

Combine like terms.

or Set each factor equal to zero

or Get the constant terms to the right side

or Take the square root of both sides of the first equation.

, or Simplify

So the zeros are , or
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