+0  
 
0
186
4
avatar+2509 

Help.

NotSoSmart  Dec 7, 2017
 #1
avatar+86921 
+2

(x - 1) (x -2) (x - 3) (x + 3)  =

 

[ x^2 - 3x + 2] [ x^2 - 9 ] =

 

x^4  -  3x^3 + 2x^2

+                 - 9x^2 +  27x - 18

________________________

x^4   -  3x^3  -  7x^2 + 27x - 18   

 

 

 4x^3  -  20x^2  +  24x   =  0       divide through by  4

 

x^3  -  5x^2  + 6x  = 0      factor

 

x (x^2 - 5x + 6)  = 0

 

x( (x - 3) (x -2)  = 0

 

The zeroes  are    0, 2 , 3

 

 

x^3  -  216  =  0        factor as a difference of cubes

 

(x - 6) (x^2  + 6x  +  36)

 

6 is a root

 

And using the quadratic formula  the other  roots will be complex

 

So we will have

 

[ -6 ±  √ [ 36 - 144] ] / 2

 

[ -6 ±  √ [  - 108] ] / 2

 

[ -6 ±  √ [  - 36 * 3 ] ] / 2

 

[ -6 ±  6i√ [  3] ] / 2

 

-3  + 3i√ 3       and  -3  - 3i√ 3

 

 

 

cool cool cool

CPhill  Dec 7, 2017
edited by CPhill  Dec 7, 2017
 #2
avatar+2509 
0

which choices are those? It don't have what you have for each one you solved..? 

3.

4.

5.

NotSoSmart  Dec 8, 2017
 #3
avatar+86921 
0

3.   third answer

4.  last answer

5.  last answer

 

cool cool cool

CPhill  Dec 8, 2017
 #4
avatar+2509 
0

Ah ok thanks!!

NotSoSmart  Dec 8, 2017

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