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Find solutions of the cubic equation:   `x^3-4x^2-3x+18=0`

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oldnick | Valedictorian

Posted April 13, 2013 at 10:48 PM via web

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Find solutions of the cubic equation:

 

`x^3-4x^2-3x+18=0`

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violy | High School Teacher | (Level 3) Assistant Educator

Posted April 14, 2013 at 4:12 AM (Answer #1)

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Using Real Zeros Theorem we will have a possible zeros: +/-1, +-/2,+/-3,+/-6,+/-9,+/-18.

Let us try x = -2. Let us use Synthetic Division.

-2|           1      -4       -3        18

+       

                        -2       12       -18

--------------------------------------

               1        -6      9          0

So, we will have (x^3 - 4x^2 - 3x + 18)/(x + 2) = x^2 - 6x + 9. 

We can factor the result as (x - 3)^2. 

Equating it to zero. 

(x - 3)^2 = 0

Take the square root of both sides. 

x - 3 = 0 

Add 3 on both sides. 

x = 3. 

Therefore, x = {-2, 3}.

     

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