We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
77
1
avatar

thanks

 Apr 15, 2019
 #1
avatar+103917 
+2

I used x instead of z.....same difference

 

If 2 + 3i is a root, then so is  2 - 3i

So

( x - (2 + 3i) )  ( x - (2- 3i)   will divide  the polyomial.....simplify.....

 

x^2 - (2 + 3i)x - (2 - 3i)x  + (2 + 3i) (2 - 3i)

 

x^2  -2x -3ix - 2x + 3ix + (4 + 9)

 

x^2 -4x + 13

 

Using synthetic division

 

                          x^2    - x   - 2

x^2 - 4x + 13  [  x^4 - 5x^3 +15x^2 -5x - 26 ]

                          x^4 -4x^3 +13x^2

                          _________________________

                                   -x^3 + 2x^2 - 5x  - 26

                                   -x^3  +4x^2 -13x

                                 ___________________

                                              -2x^2  + 8x - 26

                                              -2x^2  + 8x - 26

                                            _______________

 

 

The remaining polynomial  is   x^2 - x - 2    which factors as  ( x + 1) (x - 2)

 

Seting each linear factor to 0  and solving for  x  produces the other two roots  x = - 1   and x = 2

 

 

 

 

cool cool cool

 Apr 15, 2019

43 Online Users

avatar
avatar