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

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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) About Me  (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
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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
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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
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that the zeros are the values of "x" that make f%28x%29=0


f%28x%29=x%5E3-6x%5E2%2B4x-24 Start with the given function


0=x%5E3-6x%5E2%2B4x-24 Plug in f%28x%29=0


x%5E3-6x%5E2%2B4x-24=0 Rearrange the equation


%28x%5E3-6x%5E2%29%2B%284x-24%29=0 Group the terms into pairs


x%5E2%28x-6%29%2B%284x-24%29=0 Factor the GCF from the first group


x%5E2%28x-6%29%2B4%28x-6%29=0 Factor the GCF from the second group


%28x%5E2%2B4%29%28x-6%29=0 Combine like terms.


x%5E2%2B4=0 or x-6=0 Set each factor equal to zero


x%5E2=-4 or x=6 Get the constant terms to the right side


x=%22%22%2B-sqrt%28-4%29 or x=6 Take the square root of both sides of the first equation.


x=2i, x=-2i or x=6 Simplify


So the zeros are x=2i, x=-2i or x=6